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 ROBERT D. 
 fARHUHAR 
 
 BOOKS ON 
 ARCHITECTURE 
 
 I NIVERSITY OF CALIFORNIA 
 LOS ANGELES
 
 COLLECTED PAPERS 
 ON ACOUSTICS
 
 7\r. 
 
 eUULtijtj^ 
 
 6{J^'^*'U^^
 
 COLLECTED PAPERS 
 ON ACOUSTICS 
 
 BY 
 
 WALLACE CLEMENT SABINE 
 
 LATE HOLLIS PROFESSOK OF MA TIlKMATIf'S AND NATURAL PHILOSOPHY 
 IN HAUVAItU UNIVERSITY 
 
 CAMBRIDGE 
 ITARVARI) INIVKHSITY PRESS 
 
 LONDON : 111 Ml'IIKKV MIl.lOliD 
 
 OxFOni) rsiVKItrtlTY I'lttSS
 
 COPYRIGHT, 1922 
 HARVARD UNIVERSITY PRESS
 
 Art 
 Library 
 
 PREFACE 
 
 1 HIS volume aims to contain all the important contributions to the 
 subject of acoustics from the pen of the late Professor W. C Sabine. 
 The greater part of these papers appeared in a number of different 
 architectural journals and were therefore addressed to a changing 
 audience, little acquainted with physical science, and to whose mem- 
 bers the subject was altogether novel. Under these circumstances a 
 certain amount of repetition was not only unavoidable, but desirable. 
 Little attempt has l)een made to reiiuce this repetition but in one 
 case an omission seemed wise. The material contained in the author's 
 earliest papers on acoustics, which appeared in the Proceedings of 
 the American Institute of Architects in 1808, is repeated almost 
 completely in the paper which forms tiie first chapter of this volume; 
 it has, therefore, been omitted from this collection with the exception 
 of a few extracts which have been inserted as footnotes in the first 
 chapter. 
 
 No apology is made for the preservation of the paper from the 
 Proceedings of the Franklin Institnic, for, tliough nnieh of the ma- 
 terial therein is to be found in the earlier chapters of this volume, t lie 
 article is valuable as a summary, and as such it is recommended 
 to the reader who desires to obtain a general view of the subject. 
 
 In addition to the papers already in print at the time of the 
 author's death the only available material consisted of the manu- 
 scripts of two articles, one on Echoes, the otiier on Whispering Gal- 
 leries, and the full notes on four of the lectures on acoustics delivered 
 at the Sorbonne in tiie spring of 1917. Of this nuiterial, the first 
 pa|X'r was discarded as being too fragmentary; the second, after 
 some slight omissions juid corrections in the text inade necessary by 
 the lo.ss of a few of the illustrations, forms Chapter 11 of this volume; 
 an al)slra<-l of so nnicli of the substance of the lecture notes as had 
 not alread\' api)eared in print has i)i'eu made, of which j)art is to be 
 found in the form of an Ai)i)endix ami part is contained in some of the 
 following paragraphs. 
 
 The reader may often be j)uzzle(l by ref»'rence to works about to be 
 piililislied l)ul of w liicli no trace is to be found in I Ills \-oIuine. It is 
 
 30oS';31
 
 vi PREFACE 
 
 u nu'lanc'holy fiut that tlu'se papers were eitlier never written or else 
 were destroyed l)y their author; no trace of them can he found. The 
 extent of I lie labors of which no adequate record remains may best be 
 jutl^ed from the following extracts taken from the notes on the Paris 
 lectures just mentioned. 
 
 " On the one hand we have the problem (Reverberation) which we 
 have been discussing up to the present moment, and on the other 
 the whole f|uestion of the transmission of sound from one room to 
 another, through the walls, the doors, the ceiling and the floors; ami 
 the telei)honic transmission, if I may so call it, through the length of 
 the structure. It is five years ago since this second problem was first 
 attacked and though the research is certainly not complete, some 
 groimd has been covered. A quantitatively exact method has been 
 established and the transmission of sound through about twenty 
 different kinds of partitions has been determined. 
 
 " For example: Transmission of sound through four kinds of doors 
 has been studied; two of oak. two of pine, one of each kind was 
 paneled and was relatively thin and light; one of each kind was very 
 heav^-, nearly four centimetres thick; through four kinds of windows, 
 one of plate glass, one with connnon panes, one double with an air 
 space of two centimetres between, one with small panes set in lead 
 such as one sees in churches; through brick walls with plaster on both 
 sides; through walls of tile similarly plastered; through walls of a 
 character not common in France and which we call gypsum block; 
 through plaster on lath; through about ten different kinds of sound 
 insulators, patented, and sold in quantities representing hundreds of 
 thousands of dollars each year, yet practically without value, since 
 one can easily converse through six thicknesses of these substances 
 and talk in a low tone through three, while a single thickness is that 
 ordinarily (•inj)lo>-ed. The behavior of an air sjjace has been studied, 
 the effect of tlie thickness of this air space, and the result of filling 
 the space with sand, saw-dust and asbestos. In spite of all this, the 
 research is far from complete and many other forms of construction 
 nuist be investigated before it will be possible to publish the results; 
 these determinations must be made with the greatest exactness as 
 very important interests are involved. . . .
 
 PREFACE vii 
 
 " The research is particuhirly hiborious because resonance has a 
 special importance in a great number of forms of construction. It is a 
 much greater factor in transmission than in absorption. 
 
 " I sliall not enhirge on this sul)ject here for two reasons: first, I 
 believe tliat it is not of special interest, at least, in its present state, 
 and second, because it is not proj)er to present a formal discussion of 
 this subject while the research is still unfinished." 
 
 The last i)aragrai)h is characteristic. The severity of tlie criti- 
 cism which Professor Sabine always applied to his own productions 
 increased with time, and it is to this extreme self-criticism and re- 
 pression that we must ascribe the loss of much invaluable scientific 
 material. 
 
 'J'hanks are due to The American Institute of Architects and to 
 the editors of The American Architect, The Brickbuilder, The En- 
 gineering Record, and The Journal of the Franklin Institute, for 
 permission to reprint tlie articles which originally appeared in their 
 respective Journals. 
 
 The Editor is also greatly obliged to Dr. Paul Sabine and Mr. Clif- 
 ford M. Swan for a great deal of valuable material, and to Mr. Frank 
 Chouteau Brown for his assistance in seeing the book through the 
 press. lie is ])articularly indebted to his colleague Professor F. A. 
 Saunders for his invaluable aid in all matters touching the correct 
 presentation of the material of this volume. 
 
 Theodore LYiL\N 
 
 JEFFERSON PHYSICAL L.XBOR.VTORV 
 
 Hahvahi) Univeksity 
 Jniu-. 1!H1
 
 CONTENTS 
 
 PAGE 
 
 1. Kcvcrbcration 3 
 
 [The American Architect, 1900] 
 
 2. The Accuracy of Musical Taste in Regard to Architectural 
 
 Acoustics. The Variation in Reverberation with Variation in 
 
 Pitch 69 
 
 [Proceedings of the American Academy of Arts and Sciences, Vol. xui, No. 2, June, 
 1900J 
 
 3. Melody and the Origin of the Musical Scale 107 
 
 [yice-Prexidenliat Address, Section li, American Association for the Adranecment 
 of Science, Chicago, 1907] 
 
 4. Effects of Air Currents and of Temperature 117 
 
 [Engineering Record, Juno, 1910] 
 
 5. Sense of Loudness 1-0 
 
 [Contributions from the Jefferson Physical Laboratory, \'i>\. \iii, 1910] 
 
 6. The Correction of Acoustical Difficulties 131 
 
 [The Arrhilecturul Quarterly of Hanard University, March, 191i] 
 
 7. Theatre Acoustics 163 
 
 [The American Architect, \o]. civ, p. 257] 
 
 8. IJuilding Material and Musical Pilch 199 
 
 The liriekbuilder, \(.l. xxiii. No. 1, .laiuiary. 1914] 
 
 9. Architectural Acoustics '■219 
 
 [Journal if the Franklin Institute, January, 1915] 
 
 10. Insulation Sound 237 
 
 |77i< liriekbuilder. Vol, XXIV, No. 2. Fohniarv, 1915] 
 
 11. Whispering fJallcries 255 
 
 Ari'KNDix -77 
 
 On the Mra.surcnicnt of tlic Intensity of Sound uiiilon thoHoactionof the Uoom 
 upon the Sound
 
 COLLECTED PAPERS 
 ON ACOUSTICS
 
 REVERBERATION' 
 
 INTRODUCTION 
 
 1 HE following investigation was not undertaken at first by choice, 
 but devolved on the writer in 1895 tlu-ough instructions from the 
 Corporation of Harvard University to propose changes for remedy- 
 ing the aoouslic-al (!ifficulti(>.s in tlie lecture-room of the Fogg Art 
 Museum, a hiiiiding tluil luid just been completed. About two years 
 were sj)ent in exjierimenting on this room, and permanent changes 
 were then nuide. Almost immediately afterward it became certain 
 that a new Boston Music Ilall would lie erected, and the questions 
 arising in tiie consideration of its jilans forced a not unwelcome con- 
 tinuance of the general investigation. 
 
 No one can appreciate the condition of architectural acoustics — 
 the science of sound as applied to buildings — who has not with a 
 pressing case in hand souglit tlirough the scattered literature for 
 some safe guidance, liespousibility in a large and irretrievable ex- 
 jjenditure of money compels a careful consideration, and emphasizes 
 the meagerness and inconsistency of the current suggestions. Thus 
 the most definite and often repeated statements are such as the 
 following, that the dimensions of a room shoidd be in the ratio 
 
 2 : 3 : 5, or according to some writers, 1:1:2, and others, 2 : 3 : 4; 
 it is probable that the basis of these suggestions is the ratios of the 
 harmonic intervals in music, but the connection is untraced and re- 
 mote. Moreover, such .advice is rather difficult to a])])ly; shoidd one 
 measure tlie length to tlie l)aek or lo the front of the galleries, to the 
 Itaek or tin- front of the stage recess? Few rooms have a flat roof, 
 where should the height Ix- measured.^ One writer, wlio Iiad >eeu llie 
 Mormon Temple. reconuuencU'd that all auditt)riums l)e elliptical. 
 Sanders Theatre is by far the best auililorium in Cambridge and is 
 .semicircular in general shape, but with a recess that nuikes it almost 
 anxihing; and, on I lie ol her hand, I he leeture-rooni in the Fogg Art 
 
 ' Tlu' AiniTiian .\rrliil(it niiil Tlic Kiigioecring Hccuril, llXlii. 
 5
 
 4 REM^RBERATION 
 
 Miiseuin is also scniicirciilar, indeed was modeled after Sanders 
 Tluatre, and it was the worst. But Sanders Theatre is in wood and 
 flu- Fofig leclure-rooiii is plaster on tile; one seizes on this only to be 
 inunediatel}' reniiiKled that Sayles Ilall in Providence is largely 
 lined with wood and is bad. Curiously enough, each suggestion is 
 advanced as if it alone were sufficient. As examples of remedies, 
 may be cited the placing of vases al)Out the room for the sake of 
 resonance, wrongly suj>posed to have been the object of the vases in 
 Greek theatres, and the stretching of wires, even now a frequent 
 though useless device. 
 
 The problem is necessarily complex, and each room presents many 
 conditions, each of which contributes to the result in a greater or less 
 degree according to circumstances. To take justly into account these 
 varied conditions, the solution of the problem should be quantitative, 
 not merely qualitative; and to reach its highest usefulness it should 
 be such (hat its application can precede, not follow, the construction 
 of the building. 
 
 In order that hearing may be good in any auditorium, it is neces- 
 sary that the sound should be sufficiently loud ; that the simultane- 
 ous components of a complex sound should maintain their proper 
 relative intensities; and that the successive sounds in rapidly mov- 
 ing articulation, either of speech or music, should be clear and dis- 
 tinct, free from each other and from extraneous noises. These three 
 are the necessary, as they are the entirely sufficient, conditions for 
 good hearing. The architectural problem is, correspondingly, three- 
 fold, and in this introductory paper an attempt will be made to 
 sketch and define briefly the subject on this basis of classification. 
 Within the three fields thus defined is comprised without exception 
 the whole of architectural acoustics. 
 
 1. Loudness. — Starting with the simplest conceivable auditorium 
 — a level and open plain, with the ground bare and hard, a single 
 person for an audience — it is clear that the sound spreads in a hemi- 
 spherical wave diminishing in intensity as it increases in size, pro- 
 portionally. If, instead of being hare, the ground is occupied by a 
 large audience, the sound diminishes in intensity even more rapidly, 
 being now absorbed. The upper part of the sound-wave escapes un- 
 affected, but the lower edge — the only part that is of service to an
 
 INTRODUCTION 5 
 
 audience on a plain — is rapidly lost. The first and most obvious 
 improvement is to raise the speaker above the level of the audience; 
 the second is to raise the seats at the rear; and the third is to place a 
 wall behind the speaker. Tlie result is most attractively illustrated 
 in the Greek theatre. These changes being made, still all the sound 
 rising at any consideriiblc ;iiigle is lost through the opening above, 
 and onl.\' pari of the speaker's efforts serve the audience. When to 
 this auditorium a roof is added the average intensity of sound 
 throughout the room is greatly increased, especially that of sustained 
 tones; and the intensity of sound at the front and the rear is more 
 nearly ecpialized. If, in addition, galleries be constructed in order to 
 elevate the distant part of the audience and bring it nearer to the 
 front, we Iiavc the gcncriil lorin of the modern auditorium. The 
 problem of calculating the loudness at different parts of such an audi- 
 torium is. obviously, com])I('X, but it is perfectly determinate, and as 
 soon as the rcHecting and absorbing power of the audience and of the 
 various wall-surfaces are known it can be solved approximately. 
 Under this head will l)e considered the effect of sounding-boards, I lie 
 relative merits of different materials used as reflectors, the refrac- 
 tion of sound, and the influence of the variable temperature of 
 the air through the heating antl ventilating of the room, and similar 
 subjects. 
 
 '2. DiatortioH of Complex Sounds: Inierference and Resonance. — 
 In discussing the subject of loudni'ss the direct and reflected sounds 
 have bei'U spoken of as if always reenforcing each other when tiiey 
 come together. A moment's consideration of the nature of sound 
 will >\\n\\ (hat. as a mallei' of I'acl, it is entirely possible for tlieiu to 
 o|)l)osi' each other, 'i'he sounding l)0(iy in its forward motion sends 
 off a wave of condensation, which is immediately followed through 
 the air 1)\- a wave of rarefaction produced l)y the vil)rating body as 
 it ni()\es l)a(k. 'i'hese two \\;L\-es of opposite character taken to- 
 gether constitute u sound-wave. The source continuing to vibrate, 
 these waves follow each other in a train. Hearing in nn'nd this alter- 
 nating character of sound, it is evident that should the sound travel- 
 ing by different palll^ by reflection from different walls- — come 
 together again, I he palli> luing e(|ual in lenglli, condensation will 
 arrive at the >anie time as eoiHJensal ion, and reenforce it. and rare-
 
 (I HK\KUBKRATION 
 
 faction will, .similarly, rt'onforcc rarefaction. But should one path 
 be a little shorter Hum tlu- otiur, rarcfaclion i)y one and condensa- 
 tion l)y tlic otluT may arrive at the same time, and at this point 
 IIhtc will l)e comparative .silence. The whole room may be mapped 
 out into regions in which the sound is loud and regions in which it 
 is ftH'ble. When there are many reflecting surfaces the interference 
 is imicli more compU'X. When the note changes in pitch the inter- 
 ference .system is entirely altered in character. A single incident 
 will serve to illustrate this point. There is a room in the Jefferson 
 Physical Lal)oratory, known us the constant-temperature room, 
 that has been of the utmost service throughout these experiments. 
 It is in the center of one wing of the building, is entirely under 
 ground, even below the level of the l)asenient of the building, has 
 separate loinulations and (loui)le walls, each wall being very thick 
 and of brick in cement. It was originally designed for investiga- 
 tions in heat requiring constant temperature, and its peculiar loca- 
 tion and construction were for this ])urpose. As it was not so in 
 use, however, it was turned over to these experunents in sound, and 
 a room more suitable could not be designed. From its location and 
 construction it is extremely quiet. Without windows, its walls, 
 floor, and ceiling — all of solid masonry — are smooth and un- 
 liroken. The single door to the room is plain and flush with the 
 wall. The dimensions of the room are, on the floor, i.'il X 6.10 
 meters; its heiglit at the walls is 2.54 meters, but the ceiling is 
 slightly arched, giving a height at the center of 3.17 meters. This 
 room is here described at length because it will be frequently re- 
 ferred to, particularly in this matter of interference of sound. While 
 working in this room with a treble c gemshorn organ pipe blown by 
 a steady wind-pressure, it wsis observed that the pitch of the pipe 
 api)arently changed an octave when the observer straightened up 
 in his chair from a position in which he was leaning forward. The 
 exi)lanation is this: The organ pipe did not give a single pure note, 
 but gave a fundamental treble c accompanied by several overtones, 
 of which the strongest was in this case the octave above. Each note 
 in the whole complex sound had its own interference system, which, 
 as long as the sound remained constant, remained fixed in position. 
 It so happened that at these two points the region of silence for one
 
 INTRODT'CTIOX 7 
 
 note coincided with the region of reenforcement in tlie other, and 
 vice versa. Thus the observer in one position heard the fundamental 
 note, and in the other, the first overtone. The change was exceed- 
 ingly striking, and as the notes remained constant, the experiment 
 could be trietl again and again. With a little search it was possible 
 to find other points in the room a I wliicli the same phenomenon 
 appeared, but generally in less pertVclion. 'I"he distortion of the 
 relative intensities of the components of a chord that may thus be 
 protluced is evident. Practically almost every sound of the voice 
 in speech and song, and of instrumental music, even single-part 
 music so-called, is more or less complex, and. therefore, subject to 
 this distortion. It will be necessary, later, to show under what cir- 
 cumstances this phenomenon is a formidable danger, and how it 
 may be guarded against, and under what circumstances it is negli- 
 gible. It is evident from the above occurrence that it may be a most 
 serious matter, for in this room two persons side by side can talk 
 together with but little comfort, most of the difficulty being caused 
 by the interference of sound. 
 
 There is another phenomenon, in its occurrence allied to inter- 
 ference, liul in nature distinct — the phenomenon of resonance. 
 Both, however, occasion the same evil — the distortion of that nice 
 adjustment of the relative intensities of the components of the 
 conii)lex sounds that constitute speecii and nuisic. The phenome- 
 non of interference just discussed merely alters the distribution of 
 sound in the room, causing the intensity of any one pure sustained 
 note to be above or below the average intensity at near points. 
 Resonance, on the other hand, alters the total amount of sound in 
 the whole room and always increases it. This phenomenon is 
 noticeable at times in using the voice in a small room, or even in 
 particular locations in a large room. Perhaps its occurrence is most 
 easily obsc-rved in setting up a large church organ, where the pipes 
 nuist be readjusted for tlie i)arli(ular s])ace in wiu'cii the organ is to 
 stand, iKi iiiallcr willi liow iiiurli care the organ may lia\c been 
 assemijled ami ;i(ljii>i(il lid'oic lc.i\ing the factory. The general 
 I)heii()nienon of resouaMce is of very wide occurn-nce, not nu-rely in 
 acoustics l)ut in mori- gross meciuinics as well, as the vibration of a 
 bridge to a properly timed tread, or the excessive rolling of a boat
 
 8 RE^TRBERATION 
 
 in certain scjus. The principlf is tlio same in all eases. I'lie follow- 
 ing conception is an easy one to gnusp, and is closelj- analogous to 
 acoustical resonance: If the palm of the hand be placed on the 
 center of the surface of water in a large basin or tank and quickly 
 depressed and raised once it will cause a wave to spread, which, 
 reflected at the edge of the water, will return, in part at least, to 
 the hand. If, just as the wave reaches the hand, the hand repeats 
 its motion with the same force, it will reenforce the wave traveling 
 over the water. Thus reenforced, the wave goes out stronger than 
 before and returns again. By continued repetition of the motion 
 of the hand so timed as to reenforce the wave as it returns, the wave 
 gets to be very strong. Instead of restraining the hand each time 
 until the wave traveling to and fro returns to it, one may so time 
 the motion of the hand as to have several equal waves following 
 each other over the water, and the hand each time reenforcing the 
 wave that is passing. This, obviously, can be done by dividing the 
 interval of time between the successive motions of the hand by any 
 whole mmiber whatever, and moving the hand with the frequency 
 thus defined. The result will be a strong reenforcement of the waves. 
 If, however, the motions of the hand be not so timed, it is obvious 
 that the reenforcement will not be perfect, and, in fact, it is possible 
 to so time it as exactly to oppose the returning waves. The appli- 
 cation of this reasoning to the phenomenon of sound, where the air 
 takes the place of the water and the sounding body that of the hand, 
 needs little additional explanation. Some notes of a complex sound 
 are reenforced, some are not, and thus the quality is altered. This 
 phenomenon enters in two forms in the architectural problem: there 
 may be either resonance of the air in the room or resonance of the 
 walls, and the two cases must receive separate discussion; their 
 effects are totally different. 
 
 The word "resonance" has been used loosely as synonj-mous 
 with "reverl)eration," and even with "echo," and is so given in 
 some of the more voluminous but less exact popular dictionaries. 
 In scientific literature the term has received a very definite and 
 precise application to the phenomenon, wherever it may occur, of 
 the growth of a vibratory motion of an elastic body under periodic 
 forces timed to its natural rates of vibration. A word having this
 
 IXTRODTCTION 9 
 
 significance is necessary; and it is very desirable that the term 
 should not, even popularly, by meaning many things, cease to mean 
 anything exactly. 
 
 3. Confusion: Reverberation, Echo and Extraneous Sounds. — 
 Sound, being energy, once produced in a confined space, will con- 
 tinue until it is cither transmitted by the boundary walls, or is 
 transformed into some other kind of energj', generally heat. This 
 process of decay is called absorption. Thus, in the lecture-room of 
 Harvard University, in which, and in ])ehalf of which, this investi- 
 gation was begun, the rate of absorption was so small that a word 
 spoken in an ordinary tone of voice was audible for five and a half 
 seconds afterwards. During this time even a very deliberate 
 speaker would have uttered the twelve or fifteen succeeding sylla- 
 bles. Thus the successive enunciations blended into a loud sound, 
 through which and above which it was necessary to hear and dis- 
 tinguish the ortlerly progression of the speech. Across the room 
 this could not be done; even near the speaker it could be done onlj' 
 with an effort wearisome in the extreme if long maintained. With 
 an audience filling the room the conditions were not so bad, but 
 still not tolerable. This may be regarded, if one so chooses, as a 
 process of multiple reflection from walls, from ceiling and from floor, 
 first from one and then another, losing a little at each reflection 
 imtil ultimately inaudible. This jihcnoiuenon will be called re- 
 verlxTation, including as a special case the echo. It must be ob- 
 served, however, that, in general, reverberation results in a mass of 
 sound filling the whole room and incapable of analysis into its dis- 
 tinct reflections. It is thus more difficidt to recogiu'ze and im])()ssible 
 to locate. The term echo will Ije res«'rved for that particular case 
 in which a short, sharp soimd is distinctly repeated by reflection, 
 either once from a single surface, or several times from two or more 
 surfaces. In the general case of reverberation we are only concerned 
 with the rate of decay of the sound. In the s])eeial case of the echo 
 we are concerned not merely with its intt-nsity. Init with the interval 
 of time elapsing between the initial .sound and the moment it 
 reaches the observer. In the room mentioned as the occasion of 
 this investigation, no discrete echo was distinctly- ])ere«'])til)le, and 
 the case will serve exci-llently as an illustration of tiie more general
 
 10 RK\T-RBERATIOX 
 
 tyiM- of rcvcrlM-ratioii. AfUr proliininary gropings,' first in the 
 lih-riitiirf anil llu'ii witli st-Vi-ial optical di-vicrs for iiu-asiiring tiu- 
 intensity of sound, both were al>an(loiu'(l, llit' latter for reasons that 
 will 1m- e\|)laineil later. Instead, the rate of decay was measured by 
 nieiLsnring what was inversely proportional to it — the duration of 
 audibility of the reverberation, or, as it will be called here, the dura- 
 tion of andiliilily of the residual sound. These experiments may be 
 I'xplained to advantage even in this introductory paper, for they 
 will give more clearly than would abstract discussion an idea of the 
 nature of reverberation. Hioadly considered, there are two, and 
 only two, variables in a room shape including size, and materials 
 including furnishings. In designing an auditorium an architect can 
 give consideration to both; in repair work for bad acoustical con- 
 ditions it is generally impracticable to change the shape, and only 
 variations in materials and furnishings are allowable. This was, 
 therefore, the line of work in this case. It was evident that, other 
 t lungs being ec|ual, the rate at which the reverberation would dis- 
 ai)pt'ar was proportional to the rate at which the sound was ab- 
 sorl)e<l. The first work, therefore, was to determine the relative 
 absorbing ])ower of various substances. With an organ l)ipe as a 
 constant source of sound, and a suitable chronograph for recording, 
 the duration of audibility of a sound after the .source had ceased in 
 this room when emjjty was found to be 5.62 seconds. All the cush- 
 ions from the seats in Sanders Theatre were then brought over and 
 stored in the lobby. On bringing into the lecture-room a number 
 of cushions having a total length of 8.2 meters, the duration of 
 audibility fell to 5. .'53 seconds. On bringing in 17 meters the sound 
 in the room after the organ pipe ceased was audible for but 4.94 
 
 ' TIh' first nirtliixl fordolcrmining tlieraloof dec-ay of the sdiiiuI. ami therefore theamoiiiit 
 of nl>!u>riiliiin. was by means of a sensitive nianometric gas flame measured by a miorometer 
 toles<ii|M\ Ijiter. photngraphinK the flame was tried; but both method.s were abandoned, for 
 lliey both showed, what the unaiiled ear eoulil |)erceivc, that the suund as observed at any 
 p<iint in the room died away in a fluetuating manner, passing through maxima and minima. 
 Moroiver, they showed wlial the unaided ear had not deteetefl. but immediately afterward 
 did rccogniw, that the sound was often more intense immediately after the source ceased than 
 tiefore. .\ll this was interesting, but it rendered impossible any accurate interpretation of the 
 results obtaine<l by these or similar methods. It was then found that the ear itself aided by 
 n suitable elerlrical i'hn>nograph for recording the duration or audibility of the residual sound 
 gave a suriirisingly sensitive and accurate method of measurement. Proe. .\merican Institute 
 of .\rehilecl.s, p. .15. 1898.
 
 INTRODUCTION 11 
 
 seconds. Evidently, the cushions were strong absorbents and 
 raj)i(lly ini[)r()viiif; tlie room, at least to the extent of (liniiiiishiiiff the 
 reverberation. The result was interesting and the process was con- 
 tinued. Little by little the cushions were brought into the room, 
 and each time the duration of audibility was measured. When all 
 the seats (43G in number) were covered, the sound was audible for 
 2.03 seconds. Then the aisles were covered, and then the j)latf()rin. 
 Still there were more cushions - - almost half as many more. 'J'hese 
 were brought into the room, a few at a time, as before, and (haped 
 on a scaffolding (hat had been erected around the room, the tlura- 
 tion of the soimd being recorded e;ich lime. Finally, when all the 
 cushions from a theatre seating nearly fifteen lumdred persons were 
 placed in the room — covering the seats, the aisles, the platform, 
 the rear wall to llic ceiling — the duration of audibility of the resid- 
 ual sound was 1.1-t seconds. This experiment, recjuiring, of course, 
 several nights' work, having been completed, ail the cushions were 
 removed ami the room was in n-adiness for the test of other absorb- 
 ents. It was evident that a standard of comparison liad i)een 
 established. Curtains of chenille, 1.1 meters wide and 17 meters in 
 total length, were draped in the room. The duration of audibility 
 was then l.al seconds. Turning to the data that had just been 
 collected it appeared that this amount of chenille was equivalent to 
 30 meters of Sanders Theatre cushions. Oriental rugs, Herez, 
 Deniirjik, and Hindoostanee, were tested in a similar manner; as 
 were also cretonne cloth, canvas, and hair felt. Similar experi- 
 ments, but in a smaller room, determined the absorbing power of 
 a man and of a woman, always by determining the number of run- 
 ning meters of Sanders Theatre cushions Dial would produce tlie 
 same efTecl. This ])r()cess of c()mi)aring two alisorbents by actually 
 substituting one for the other is laborious, and it is given here only 
 to show the first steps in the development of a method that will be 
 expanded in the following papers. 
 
 In this lecture-room felt wius finally placed permanently on i)ar- 
 ticular walls, and the room was rendered not excellent, but entirely 
 serviceable, and it has been used U)v the pa>l tiu-ee yi-ars without 
 serious complaint . It i^ not inltiidcd to discuss this particular case 
 in the introductory paper. becau,se such discu.ssion would i>e prema-
 
 li R?:\TRBKRATK)\ 
 
 tun- aiul logically inconipK-ti'. It is mentioned here iiierely to illus- 
 trate concretely the subject of reverberation, and its dependence on 
 absorpti*>n. It would be a niislake to suppose tliat an absorbent is 
 ulwavs desirable, or even when desirable that its position is a matter 
 of no consequence.' 
 
 While the logical order of considering the conditions contributing 
 to or interfering with distinct hearing would be that enijjloyed above, 
 it so hai)pens that exactly the reverse order is jjreferable frcmi an 
 exi)erinienlal standpoint. By taking up the subject of reverberation 
 first it is possible to determine the coefficients of absorption and 
 reflwtion of various kinds of wall surface, of furniture and draperies, 
 and of an audience. The investigation of reverberation is now, after 
 five years of exi)erimental work, comj>leted, and an account will be 
 rendered in the following papers. Some data have also been secured 
 on the other to|)ics and will be published as soon as rounded info 
 definite form. 
 
 This paper may Ik- n-garded ius introductory to the general sub- 
 ject of architectural acoustics, and immediately introductory to a 
 series of articles dealing with tlie subject of reverberation, in which 
 the general line of procedure will be, briefly, as follows: The absorb- 
 ing power of wall-surfaces will be determined, and the law according 
 to which the reverberation of a room depends on its volume will be 
 demonstrated. The absolute rate of decay of the residual sound in 
 a number of rooms, and in the same room under different conditions, 
 will then be determined. In the fifth paper a more exact analysis 
 
 ' Tlicrc is no simple Irc.itment tlial ciiii cure all cases. There may be ina<lequate absorption 
 anil prolonged residual sound; in this case absorbing material should be added in the proper 
 places. On the other hand, there may be excessive absorption by the nearer parts of the hall 
 and by the nearer audience and the sound may not penetrate to the greater distances. Ob- 
 viously the treatment should not be the same. There is such a room belonging to the Uni- 
 versity, known hx-ally as Sever 35. It is low and long, .\cross its ceiling are now stretched 
 huniire<is of w ires and many yards of cloth. The former has the merit of being harmless, the 
 latter is like bleeiling a patient suffering from a chill. In general, should the sound seem 
 smothered or loo faint, it is because the sound is either imperfectly distributed to the audience, 
 or is tost in waste places. The first may occur in a very low and long room, the second in one 
 with a very high ceiling. The first can be remedied only slightly at best, the latter can be im- 
 proved by the use of reflectors behind and above the speaker. On the other hand, should the 
 sound be loud but confuscil, due to a perceptible prolongation, the difficulty arises from there 
 being reflecting surfaces either too far distant or improperly inclined. Proc. .\merican Insti- 
 tute of .\rcliitects. p. 39, 1898.
 
 ABSORBING POWER OF WALL-SLTiFACES 13 
 
 will be given, and it will be shown that, by very different lines of 
 attack, starting from diflFerent data, the same numerical results are 
 secured. Tables will be given of the absorliing power of various 
 wall-surfaces, of furniture, of an audience, and of all the materials 
 ordinarily found in any (luaiilily in an auditorium. Finally, in 
 illustration of the calculation of reverberation in advance of con- 
 struction, will be cited the new Boston Music Hall, the most interest- 
 ing case that has arisen. 
 
 ABSORBIXC; POWER OF WALL-SURFACES 
 
 In the introductory article the problem was divided into considera- 
 tions of loudness, of distortion, and of confusion of sounds. Con- 
 fusion may arise from extraneous disturbing sounds — street noises 
 and the noise of ventilating fans — or from the prolongation of the 
 otherwise discrete sounds of nuisic or the voice into the succeeding 
 sounds. The latter phenomenon, known as reverberation, results 
 in what may be called, with accuracy and suggestiveness, residual 
 sound. The (Imalion of I his residual .sound was shown to depend 
 on the amount of ab.sorbing material inside the room, and also, of 
 course, on the absorbing and transmitting power of the walls; and 
 a method was outlined for tleternu'ning the absorbing power of the 
 former iu terms of the absorbing power of some material chosen as 
 a standard and used in a preliminary calibration. A moment's con- 
 sideration demonstrates that this method, which is of the general 
 type known as a "substitution method," while effective in the de- 
 termination of the absorbing power of furniture and corrective 
 material, aiul, in general, of anything that can be brought into or 
 removed from a room, is insufficient for determinating the absorb- 
 ing jiower of wall-surfaces. 'J'his, the absorbing power of wall- 
 surfaces, is the subjt'cl of the present ])ai)er; aiul as the method of 
 determination is an evlensiou of llic abovi' work, an<l finds its justi- 
 fication in the striking consistency of the results of the observations, 
 a nu)re clal)orate description of the experimental method is desirable. 
 A proof of the accuracy of every step taken is especially necessary 
 in a subject concerning which theory luus been so largely uncon- 
 trolled speculation.
 
 1 I UKVKHBKRATIOX 
 
 Kiirly ill tlic invest ipitioii if was found tliat nu-asurenients of 
 tlu" IfiiK'li of *'""' <liiriiif,' which u sound was au(lil)k' after tlie source 
 had erased gave j)roniising results whose larger inconsistencies could 
 1m' trac-<'d directly to the distraction of outside noises. On repeating 
 the work during the most ((iiiet part of the nigiit, between half-past 
 twelve and five, and using refined recording apparatus, the minor 
 irregidarities, due to n-laxed attention or other personal variations, 
 were surprisingly small. To seciin- accuracy, however, it was neces- 
 sary to suspend work on the apjiroach of a street car within two 
 blocks, or on the p;ussing of a train a mile distant. In Cambridge 
 these interruptions were not serious; in Boston and in New York 
 it was necessary to snatch observations in very brief intervals of 
 c|uiet. In every case a single determination of the duration of the 
 residual sound was based on the average of a large number of 
 observations. 
 
 An organ pijie, of the gemshorn stop, an octave above middle c 
 (51'-2 vibration fre(|uencv) was used as the source of .sound in some 
 preliminary experiments, and has been retained in subsequent work 
 in the absence of any good reason for changing. The wind supply 
 from a double tank, water-sealed and noiseless, was turned on and 
 off the organ i)ii)e by an electro-pneumatic valve, designed by ^Vlr. 
 George S. Ilutchings. and similar to that u.sed in his large church 
 organs. The electric current controlling the valve also controlled 
 the chronograph, and was made and broken by a key in the hands 
 of the observer from any part of the room. The chronograph em- 
 ployed in the later experiments, after the more usual patterns had 
 l>een tried and discarded, was of sjx'cial design, and answered well 
 the requirements of the work — perfect noiselessness, portability, 
 and capacity to measure intervals of time from a half second to ten 
 seconds with considerable accuracy. It is shown in the adjacent 
 diagram. The current whose cessation stopped the sounding of the 
 organ pii)e also gave the initial record on the chronograph, and the 
 only duty of the observer was to make the record when the sound 
 ceased to be audible. 
 
 While the supreme test of the investigation lies in the consistency 
 and simi)licity of the whole solution us outlined later, three pre- 
 liminary criteria are found in (1) the agreement of the observations
 
 ABSORBINC; POWER OF WALL-SURFACES 
 
 15 
 
 ol)tiiined at one sitting, ('-2) the agreement of the results obtained 
 on different niglits and after tlie lapse of months, or even years, l)y 
 the same observer under simihir conditions, and (3) the agreement 
 of independent determinations by different observers. The first 
 can best be discussed, of course, by the recognized physical methods 
 for examining the accuracy of an extended series of observations; 
 
 l*'l<:. !. <'lin)n()^ni])Ii, l)aU»T\', and air rcst-rvoir, Ihr liiltrr surniounti'd 
 l).v llir rli<lr(>-|)ii<iiiiiatit' valve and orpin pipe. 
 
 and the result of such cxanu'nation is as follows: Each dctcruiiualion 
 being I lie incaM of aixiul Iwcuty ()bscr\al ions uiidi-r conditions such 
 thai llic audililc diiialiOu of llic loichial souiui was 4 seconds, the 
 average devialioii of llic single ol>ser\ations from the mean was .11 
 seconds, and the maximum de\iation was .31. The ctJinputed 
 "j)robable error" of a single determination Wius about AH seconds; 
 .IS a mailer of fact, the average tleviation of t«'n determinations 
 from I lie mean of I he leu was .03 seconds, and the iiia\imuiii de\i-
 
 16 hkvi;i{|{i;hatiox 
 
 at ion was .().>. Tlif roason for this accuracy will l)e discussed in a 
 suhsoqut'iit pajMT. The prohal)lc error of the mean, thus calculated 
 from the tleviatious of the single ol).servations, covers only those 
 variaMe errors as likely to increase as to decrease the final result. 
 Fixed iiislninH-ntal errors, and the constant errors commonly re- 
 ferretl to by the term "personal factors" are not in this way exposed. 
 They were, however, rejjeatedly tested for by comparison with a 
 dock l>eatiMf; seconds, and were very satisfactorily shown not to 
 amount to more than .0^2 seconds in their cunmlative eft'ect. Three 
 typ«'s of chronographs, and three kinds of valves between the organ 
 j)ipe and the wind chest were used in the gradual development of 
 the experiment, and all gave for the same room very nearly the same 
 final results. The later instruments were, of course, better and more 
 accurate. 
 
 The second criterion mentioned above is abundantly satisfied by 
 the experiments. Observations taken every second or third night 
 for two months in the lecture-room of the Fogg Art ^Museum gave 
 practically the same results, varying from .5.45 to o.G-Z with a mean 
 value of 5.57 seconds, a result, moreover, that was again obtained 
 after the lapse of one and then of three years. Equally satisfactory 
 agreement was obtained at the beginning ami at the end of tlu^ee 
 years in Sanders Theatre, and in the const ant -temperature room 
 of the Physical Laboratory. 
 
 Two gentlemen, who were already somewhat skilled in physical 
 observation, Mr. Gifford LeClear and Mr. E. D. Densmore, gave 
 the necessary time to test the third point. After several nights' 
 practice their results differed but slightly, being .08 .seconds and 
 .10 seconds longer than those obtained by the writer, the total 
 duration of the sound being 4 seconds. This agreement, showing 
 that the results are i>robably very nearly those that would be ob- 
 tained by any auditor of nornud hearing, gives to them additional 
 interest. It should be stated, however, that the final development 
 of the subject will adapt it with perfect generality to either normal 
 or abnormal acuteness of hearing. 
 
 Almost the first step in the investigation was to establish the 
 following three fundamentally important facts. Later work has 
 proved these fundamental facts far more accurately, but the original
 
 ABSORBING POWER OF WALL-SURFACES 
 
 17 
 
 experiments are here given as being those upon which the conclu- 
 sions were based. 
 
 The duration of audibility of the residual sound is nearly the same 
 in all parts of an auditorium. — Early in the investigation an ex- 
 periment to test this point was made in Steinert Hall, in Boston. 
 The source of sound remaining on the platform at the point marked 
 
 Fig. 2. Steinert Hall, Boston : position of air reservoir 
 and organ pipe at (); ixisitions of observer 1-8. 
 
 in the diagram, observations were made in succession at the points 
 marked 1 to 8, with the results shown in the table: 
 
 Station 
 
 1 
 
 2 
 
 8 
 
 4 
 
 Durutioi) 
 
 Slatiou 
 
 Duratioo 
 
 2.12 
 
 5 
 
 2.23 
 
 2.17 
 
 6 
 
 2.27 
 
 2.23 
 
 7 
 
 2.20 
 
 2.20 
 
 8 
 
 2.26 
 
 Oil first in.spection these results seem to indicate that the duration 
 of audibility is very slightly greater at a distance from the source, 
 and it would be easy to explain this on the theory that at a distance 
 the ear is less exhau.sted by the rather loud noise while the i)ipe is 
 sounding; but, ius a matter of fact, tliis is not the ease, and the
 
 18 
 
 in;M:Hi{KHA'riox 
 
 variations tluTc sliown arc williiii the limits of accuracy of the 
 a|)|)aratiis (•iii|)l()yf(l and the stcill attained tlnis early in the in- 
 vest i>;at ion. Numerous later experiments, more accurate, hut not 
 especially directed to this point, have verified the above general 
 statement {|uite conclusively. 
 
 The duration of audihUUy is ncarlij iudepetideut of Ihc position of 
 the souri-r. 'Die oli^crvrr remaining; at the point marked in the 
 
 diafiram of the large lecture-room 
 of the Jefferson Physical Labora- 
 tory, the organ i)ij)e and wind chest 
 were moved from station to sta- 
 tion, as indicated l)y the ninnljcrs 
 1 to (i, witli the results shown in' 
 the table: 
 
 Station Duration 
 
 1 3.90 
 
 ■2 4.00 
 
 :? 3.90 
 
 4 3.98 
 
 ,"> 3.95 
 
 (i 3.96 
 
 m 
 
 R 
 
 a 
 
 R 
 
 R 
 
 H 
 
 1 
 
 ^^^ 1 M M II II II 1 1 
 
 "-- — sl 
 
 nODOS 
 
 •> 
 
 UUUuL 
 
 
 
 
 1 
 
 3 "„"" 
 
 ,. , , . , ,, r.1 ■ , The cfficiencij of an absorbent in 
 
 rl<i. .». Lfcturf-r<)<)tii. Ji-ticrson I'hysical _ _ 
 
 ljiU)ratory: position of obsi-rvcr at 0; reducing the duration of the residual 
 
 position., of air n-MTVoir and organ pipe ^.,^,^,,^, '-^.^ ^^„^;^^ ordinary cirCUm- 
 
 stances, nearly independent of its 
 position. — Fifty meters of cretonne dotli drajjcd on a scaffolding 
 under the rather low ceiling at the back of the lecture-room of 
 the Fogg Museum, as shown in the next diagram, reduced the 
 audil)le duration of the residual sound by very nearly the same 
 amount, regardless of the section in which it hung, as shown in the 
 following table, the initial duration being 5.57 seconds: 
 
 Section 
 1. . 
 
 2.. 
 3.. 
 4.. 
 
 Duration 
 
 . 4.88 
 
 . 4.83 
 
 . 4.92 
 
 . 4.85 
 
 In some later experiments five and a half times as much cretonne 
 draped on the scaffolding reduced the audible duration of the
 
 ABSORBING POWER OF WALL-SURFACES 
 
 1!) 
 
 residual .sound to 3. "25 seconds; and when hung fully exposed in 
 the high dome-like ceiling, gave 3.29 seconds, confirming the above 
 statement. 
 
 These facts, simple when proved, were by no means self-evident 
 so long as the problem was one of reverberation, that is, of succes. 
 sive reflection of sound from wall to 
 wall. Tlie\- indicated that, al Icaslwilli 
 reference to auditoriums of not too 
 great diincnsions, another jioint of view 
 woukl be more suggestive, that of re- 
 garding the whole as an energy problem 
 in which the source is at tlie organ 
 pipe and the decay at the walls and 
 at tlie contained absorbing material. 
 The above results, then, all point to 
 the evident, but pcrliajis not appreci- 
 ated, fact that the dispersion of sound 
 between all j)arts of a hall is very nipid 
 in comparison with the total time re- 
 quired for its complete absorjjfion, and 
 tiiat in a very short time after the 
 source has cea.sed the intensity of the 
 residual sound, except for the phenom- 
 enon of interference to be considered 
 later, is very nearly the same every- 
 where in the room. 
 
 I'liis much being determined, the 
 investigation was continued in the fol- 
 lowing manner: Cushions from San- 
 ders Theatre were transferred to llie 
 lobby of I lie lecture-room of the J''ogg 
 ]V[u.seum; a very few were brought into the room and spread along 
 the front row of seats; the duration of audiltilily of the residual 
 sound, diminished 1)_\ llic inl iddiiclioii of lliis additional al)sorbeiit, 
 was determined, and liie total length of cushion was measured. The 
 next row of seats was then (•<)vere<l in the sanii- manner and the two 
 observations made length of cushion and iluration of resitlual 
 
 Fig. i. Lectur»'-room, Fopg .\rt 
 Museum: position of ob.sorvcr at 
 (); positions of absorbent ul 1-4, 
 ami in tlie dome.
 
 20 HEVKIiHKHATIOX 
 
 sound. Tliis was rciH-atcd till cushions covered all the seats. This 
 work wjui at first undertaken solely with the intention of determin- 
 ing the relative merits of different absorbing materials that might 
 be plac-e<l in the room !is a corrective for excessive residual soimd, 
 and the aeeounl of this ai)plieation is ffWcn in the introductory 
 paper. A subsequent study of these and similar results obtained in 
 many other rooms has shown their applicability to the accurate 
 (1. hrmination of the absorbing luiwcr of wall-surfaces. This appli- 
 cation may be shown in a i)urely analytical manner, but the expo- 
 sition is greatly helped by a graphical representation. The nuxnner 
 in which the tluralion of the residual sound in the Fogg lecture- 
 room is dependent on the amount of absorbing material present is 
 shown in the following table: 
 
 UiiRth Duration of 
 
 of Cushion Residual Sound 
 
 in MclCTJ "■ i^onds 
 
 5.61 
 
 8 5.33 
 
 17 4.94 
 
 38 4.56 
 
 44 4.21 
 
 63 3.94 
 
 83 3.49 
 
 104 3.33 
 
 128 3.00 
 
 145 2.85 
 
 162 2.64 
 
 189 2.36 
 
 213 2.33 
 
 242 2.22 
 
 This table, represented graphically in the conventional manner — 
 length of cushion jilotted horizontally and duration of sound verti- 
 cally — gives points through which the curve may be drawn in the 
 accompanying diagram. To disco\'er the law from this curve we 
 represent the lengths of cushion by .r, and the corresponding dura- 
 tions of sound, the vertical distances to the curve, by t. If we now 
 seek the formula connecting .r and t that most nearly expresses the 
 relationship represented by the above curve, we find it to be 
 (a -|- x)t = k, which is the familiar formula of a rectangular hyper- 
 bola with its origin displaced along the axis of .r, one of its asymp- 
 totes, by an amount a. To make this formula most closely fit our
 
 ABSORBING POWER OF WALL-SURFACES 
 
 21 
 
 curve we must, in this case, give to the constant, a, the numerical 
 value, 146, and to /.• tlie value, 81.'5. The accuracy with which the 
 formula represents the curve may be seen by comparing the dura- 
 tions calculated by the formula with those determined from the 
 curve; they nowliere diiVer by more than .04 of a si-cond, and ha\e, 
 on an average, a difference of only .02 of a second. This is entirely 
 satisfactory, for the calculated points fall off from the curve by 
 scarcely the l)readth of the pen jjoint with which it was drawn. 
 
 The determination of the ab.sorbing power of the wall-surface 
 depends on the interpretation of the constant, a. In the formula, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 '"^^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 •A. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■^ 
 
 
 ^-, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■"— 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 9 
 
 8 
 7 
 6 
 5 
 4 
 3 
 2 
 1 
 
 "20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 
 
 Length of cushions in meters 
 
 Fig. 5. Curve showing the relation of tlie duration of the residual 
 sound to the added absorbing material. 
 
 the position of a, indicating that x is to be atlded to it, suggests 
 that .(■ and a are of a like nalurc, and llial <t is a measure of the 
 absorbing power of the bare room; in order to determine the curve 
 this was increa.sed by the introduction of the cushions. This is 
 even better shown by the diagram in which the portion of the curve 
 experimentally determined is fitted inio llie curve as a whole, and 
 a and x are indicated. Thus, the absorbing power of the room — 
 the walls, partly plaster on stone, partly plaster on wire lath, the 
 windows, the skyliglil, I lie floor — was equivalent lo 14(» rimning 
 meters of Sanders Theatre cushions. 
 
 The last .statement shows llir necessity for two Mib>i(li:iiy in- 
 vestigations. The first, to express the residts in .some more i)ernia- 
 nent, more tmiversally availal)le, and, if po.ssible, more ab.solute
 
 o^ 
 
 HKVKHHKRATION 
 
 unit Ihiin llu- cushions; tlic otIuT, lo apimrlioii tin- total al)sorbing 
 power aiMonj,' tin- various conipoiu'nt.s of the structure. 
 
 Tlif transformation of results from one system of units to an- 
 otlier necessitates a careful study of both systems. Some early 
 experiments in \vlu<-li the cushions were placed with one edfje pushed 
 jigaiust the hacks of the settees gave results whose auonuilous 
 character suggested that, perhaps, their absorbing power depended 
 not merely on the amount present but also on the area of the sur- 
 face exposed. It was then recalled that about two years before, 
 at the beginning of an evening's work, the first lot of cushions 
 
 10 
 
 s 
 
 ■S T 
 
 c 
 
 .5 5 
 
 c 
 .2 i 
 
 S 
 
 = 3 
 2 
 1 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 '' 
 
 [S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — — 
 
 — 
 
 — 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 so 
 Walls 
 
 160 
 
 240 S20 400 
 
 Cushions 
 
 S60 
 
 Fig. 6. Curve 5 plotted as part of its eorresponding rectangular 
 hypcrlx)la. The solid part was determim^d experimentally; 
 the displacement of this to the right measures the absorbing 
 power of the walls of the room. 
 
 brought into the room were placed on the floor, side by side, with 
 edges touching, but that after a few observations had been taken 
 the cushions were scattered about the room, and the work was 
 rei)eate(l. This was done not at all to uncover the edges, but in 
 the primitive uncertainty as to whether near cushions would draw 
 from each other's supply of soimd, as it were, and thus diminish 
 each other's efficiency. No furl li.i- t bought was then given to these 
 discarded observations until recalled by the above-mentioned dis- 
 crejjancy. 'J'hey were sought out from the notes of that period, 
 and it was found that, a.s suspected, the absorbing power of the 
 cushions when touching edges was less than when separated. Eight 
 cushions had been used, and, therefore, fourteen edges had been
 
 ABSORBING POWER OF WALI^SURFACES 23 
 
 touching. A record was found of the length and the breadth of 
 the cushions used, and, assuming that the absorbing power was 
 proportional to the area exposed, it was possible to calculate their 
 thickness by comparing the audible duration of the residual sound 
 in the two sets of observations; it was thus calculated to be 7.4 
 centimeters. On stacking up the same cushions and measuring 
 their total thickness, the average thickness was found to be 7.2 
 centimeters, in very close agreement with the thickness estinuited 
 from their absorption of sound. Therefore, the measurements of 
 the cushions should be, not in running meters of cushion, but in 
 square meters of exposed surface. 
 
 For the purposes of the present investigation, it is wholly un- 
 necessary to distinguish between the transformation of the energj- 
 of the sound into heat and its transmission into outside space. 
 Both shall be called absorption. The former is the special accom- 
 plishment of cushions, the latter of open windows. It is obvious, 
 however, that if both cushions and windows are to be classed as 
 absorbents, the open window, because the more universally acces- 
 sible and the more permanent, is the better unit. The cushions, on 
 the other hand, are by far the more convenient in practice, for it 
 is possible only on very rare occasions to work accurately with the 
 windows open, not at all in summer on account of night noises — 
 the noise of crickets and other insects — and in the winter only 
 when there is but the slightest wind; and further, but few rooms 
 have sufficient window surface to produce the desired absorption. 
 It is necessary, therefore, to work willi cushions, but to express the 
 results in open-window units. 
 
 Turning now to the unit into which the results are to be trans- 
 formed, an especially quiet winter night wjis taken to determine 
 whether the absorbing power of open windows is jjroportional to 
 the area. A test of tiie absorbing power of seven windows, each 
 1.10 meters wide, when oix-iied ."-iO, .40, and .80 meter, gave results 
 that are plotted in tiie diagram. The points, by falling in a straight 
 line, show that, at least for moderate i)readlhs, the al)sorbing 
 power of open windows, as of cushions, is accurately proi)ortional 
 to tlie area. Ex|)i'riments in several rooms especially convenient 
 for the purpo.se determined the absorbing power of the cushions to
 
 ^4 
 
 RKVKHHKRATIOX 
 
 Ix- .80 of that of an (-(lual art-a of opt-n windows. Tlu-.so cusiiions 
 wiTf of hair, covtrcd witli canvius and light dunia.sk. "Elastic 
 Felt" cu-shions having lufii ii>*«'d during an investigation in a New 
 York church, it wjw necessary on returning to Cand)ridgc to deter- 
 mine their ai>sorl)iiig power. This was acconii)iished through the 
 c-ourtesy of the manufacturers, Messrs. Sperry & Beale, of New 
 York, and the absorbing power was found to be .73 of open-window 
 
 u 
 
 t 
 • 
 
 I* 
 
 "t 4 
 
 < 3 
 2 
 
 1 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f\ 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .1 
 
 J .2 
 
 B Ji 
 
 .4< 
 
 .» 
 
 .« 
 
 3 .7 
 
 > .8< 
 
 9 .»< 
 
 ) 1.00 1.10 1.20 130 1.40 1. 
 
 Open window 
 
 Fig. 7. The absorbing power of open windows plotted against the 
 areas of the openings, showing them to be proportional. 
 
 units — an interesting figure, since these cushions are of frequent 
 use and of standard cliaracfer. 
 
 Hereafter all results, though ordinarily obtained by means of 
 cushions, will be expres.sed in terms of the absorbing power of open 
 windows — a unit as permanent, universally accessible, and as 
 nearly absolute as possible. In these units the total absorbing 
 power of the walls, ceiling, floor, windows and chairs in the lecture- 
 room of the Fogg Museum is 75. .5. 
 
 Next in order is the apportionment of the total absorbing power 
 among the various components of the structure. Let ^i be the area 
 of the plaster on tile, and fli its absorbing power per square meter; 
 Si and «2 the corresponding values for the plaster on wire lath; S3 
 and 03 for window surface, etc. Then 
 
 «! «1 + 02 «2 + 03 ^3 + Oi Si, ctc. = 75.5, 
 
 Si, St, S3, etc., are known, and «i, «2, 03, etc. — the coeflBcients of 
 absorption — are unknown, and are being sought. Similar equa-
 
 APPROXIMATE SOLUTION 
 
 25 
 
 tions may be obtained for other rooms in which the proportions 
 of wall-surface of the varioiis kinds are greatly different, until there 
 are as many equations as there are unknown quantities. It is then 
 possible by elimination to determine the absorbing power of the 
 variou.s materials used in construction. 
 
 Through the kindness of Professor Goodale, an excellent oi)por- 
 tunity for securing some fundamentally interesting data was 
 afforded by the new Botanical Laboratory and Greenhouse recently 
 given to the L^niversity. These rooms — the office, the laboratory 
 and the greenhouse — were exclusively finished in hard-pine sheath- 
 ing, glass, and cement; the three rooms, fortunately, combined the 
 three materials in very tlifferent proportions. I'hey antl the con- 
 stant-temperature room in the Physical Laboratory — the latter 
 being almost wholly of brick and cement — gave the following 
 data: 
 
 Area of 
 Hard Pine 
 Sheathing 
 
 Area of Glaas 
 
 Area of Brick 
 aod Cement 
 
 Combined 
 
 Absorbing 
 
 Power 
 
 Office 
 
 127.0 
 
 84.8 
 
 12.7 
 
 2.1 
 
 7 
 
 6 
 
 80 
 
 
 
 
 
 30 
 
 So 
 
 124 
 
 8.37 
 
 l.alHiratory 
 
 Grci'iihouso 
 
 Constant-temperature room . . . . 
 
 5.14 
 4.C4 
 3.08 
 
 This table gives for the three components the following coefficients 
 of absorption: hard pine sheathing .058, glass .024, brick set in 
 cement .023. 
 
 APPROXIMATE SOLUTION 
 
 In the preceding paper it was shown that the duration of the 
 residual sound in a particular room was proi)orti(>nal inversely to 
 the absorbing power of the bounding walls and tlic contained 
 material, the law being expressed closely by the fornuda {a + x)t 
 = Jc, the formula of a displaced rectangular hyjHrbola. In the 
 present paper it is proposed to show that this fornuda is general, 
 and ajJijlicable to any room; that in adapting it to different rooms 
 it is only necessary to change the value of the et)nstant of inverse 
 proportionality /.•; tlmt /,• is in turn proportional to the volume of
 
 ^.Mi 
 
 RE^TRBERA^'I()X 
 
 ll„- n«.m. iK'ing equal to about .171V in the present experiments, 
 hut ch-peiident on the initial intensity of the sound; and finally, 
 that hv sul)stiluting I lie value of k thus determined, and also the 
 
 ^ a 
 
 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \! 
 
 ■n 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 --■^ 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 =*=: 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 "l 
 
 
 
 
 
 
 
 
 S.^ 
 
 ~7 . 
 
 
 
 , 
 
 ^. 
 
 
 "^^ 
 
 
 
 
 
 ■==! 
 
 =y: 
 
 ~S, 
 
 
 
 
 
 
 
 -^ 
 
 
 ^^ 
 
 r^ 
 
 =— 
 
 ■-2-. 
 
 
 -1-. 
 
 
 
 
 
 
 
 = 
 
 
 
 
 
 
 
 
 
 ___ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 t 
 
 I 
 
 i 
 
 i 
 
 i 
 
 i 
 
 ' 
 
 » 
 
 9 10 11 12 
 
 L3 19 1 
 
 Longth of cushions in meters 
 
 Fig. 8. Curves showing the relation of the duration of the residual 
 sound to the added absorbing material, — rooms 1 to 7. 
 
 c 
 
 e 
 .S 2 
 
 
 — ^ 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 "^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 K 
 
 
 
 
 "-- 
 
 -11. 
 
 
 
 
 
 
 
 
 tir^ 
 
 ^8, 
 
 -12- 
 
 
 
 , 
 
 
 
 
 
 
 
 
 
 
 " 
 
 
 H 
 
 
 
 
 
 
 
 
 ■^ 
 
 
 
 
 
 
 
 
 
 "*" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 20 30 «0 $0 60 TO 80 90 100 110 UO 130 140 150 
 
 Length of cushions in meters 
 
 Fig. 9. Curves showing the relation of the duration of the residual 
 sound to the added absorbing material, — rooms 8 to 12. 
 
 value of a, the absorbing power of the walls, and of x, the absorbing 
 power of the furniture and audience, it is possible to calculate in 
 advance of construction the duration of audibility of the residual 
 sound.
 
 APPROXI.MATE SOLUTION 
 
 27 
 
 The truth of the first proposition — the general appUcahiUty 
 of the hyperbohc hiw of inverse proportionaUty — can be satis- 
 factorily shown by a condensed statement of the results obtained 
 from data collected early in tiie investigation. These observations 
 were made in rooms varying extremely in size and shape, from a 
 small committee-room to a theatre having a seating capacity for 
 nearly fifteen hundred. Figures 8 and 9 give the curves experi- 
 mentally determined, the duration of audibility of the residual 
 
 10 20 30 40 50 60 TO 80 90 100 110 120 130 140 160 
 120 160 240 300 360 420 
 S40 720 900 1080 1360 
 
 Total absorbing material 
 
 Fig. 10. The curves of Figs. 8 and !) enteretl as parts of their corre- 
 sponding rectangular h\-perlx)las. Thre<; .scales are employed for 
 the volumes, by groups 1-7, 8-11, and H. 
 
 sound l)eing plotted against running meters of cushions. Two 
 diagrams are given in order to employ a smaller .scale for the larger 
 rooms, this scale l)eing one-tenth the other; and even in this way 
 there is shown but one-quarter of the curve actually obtained in 
 rooms numbered 11 and l'-2, the Fogg Art Museum lecture-room 
 and Sanders Theatre. In Fig. 10 each curve is entered as a i)arl 
 of its corresi)onding hyperbola referred to its asymptotes as axes. 
 In this case three scales are employed in order to show the details 
 luor*' clearly, the results oljtaincd in rooms 1 to 7 on one scale. S to 
 1 1 on another, and l'-2 on a third, the three scales being proj)ortionaI 
 to one, three and nine. The continuous i)ortions of the curves 
 show the |>,irts (Ictcrniiiied cxpcriMifulallx'. V.ViW with the scale
 
 ?8 
 
 RK\ KUBKHATIOX 
 
 thus clianRcd only a very small portion of the experimentally de- 
 termined i.arts of eurves 11 ami hi are shown. Figures 11 to 10, 
 inelusive. all drawn to the same scale, show the great variation in 
 size and shai)e of the rooms tested; and the accompanying notes 
 ^ive for ( iich the maximum dei)arture and average departure of the 
 curve, exi)eriineiilally determined, from the nearest true liyi)erbola. 
 1. Committee-room, I'niversity Hall; plaster on wood lath, 
 wood dado; volume, 65 cubic meters; original duration of residual 
 sound before the introduction of any cushions, 2.82 seconds; maxi- 
 
 
 
 " 
 
 
 BB 
 
 
 
 
 a 
 
 no 
 
 ! 1 
 
 
 
 a 
 
 
 
 lit ■ 1 u 
 
 |q 1 11-11 J| 
 
 4 
 
 
 1 
 
 
 
 
 n 
 
 
 W 
 
 n 
 
 
 
 1 
 
 
 
 IP i 1 CD 1 1 (—1 
 
 1 1 
 
 C 
 
 lot 1 [=1 1 1 1 ID ( 111 
 
 5 6 7 
 
 Fig. 11. 1. CommiUpc-room. 4. Laboratory, Hotanic Gardeu.s. 3. Office, 
 Hotaiii((!ar(l(ii.s. i. Hcoordcr's Ofike. 5. Greenliou.se. 6. Dean's 
 H<M>m. 7. Clerk's RiHini. 
 
 iinmi departure of experimentally determined curve from the nearest 
 hyperbola, .0!) second; average dej)arture, .03 second. 
 
 2. Laboratory, Botanic Gardens of Harvard University; hard 
 pine walls and ceiling, cement floor; volume, 82 cubic meters; 
 original duration of the residual sound, 2.39 seconds; maximimi 
 departure frdiii hyperbola, .09 second; average departure, .02 
 second. 
 
 3. Office, Botanic Gardens; hard pine walls, ceiling and floor; 
 volume, 99 cubic meters; original duration of residual sound, 1.91 
 .seconds; maximum departure from hyperbola, .01 second; average 
 departure. .00 second. 
 
 4. Recorder's OfKce, University Hull; i)laster on wood lath. 
 wood dado; volume, 102 cubic meters; original duration of residual 
 sound, 3.68 seconds; maximum departure from hyperbola, .10 
 second; average departure, .04 second.
 
 APPROXnrATE SOLUTION 
 
 29 
 
 5. Grot'iihousc, Botanic Gardens; glass roof and sidos, cement 
 floor; volume, l;54 eubie meters; original duration of residual 
 
 l'"iG. IZ. I'uculty-room. 
 
 sound, 4.40 seconds; maximum departure from hyperbola, .08 
 
 second; average dejjarture, .0.'5 second. 
 
 G. Dean's Room, University Hall; ])lasler on wood lalh, wood 
 dado; volume, 166 cubic meters; original duration of residual 
 
 Fig. 13. I^'oturc-rooin. 
 
 sound, 3.38 seconds; maxinunii (le])arlure from hyperbola, .06 
 second; average departure, .01 second. 
 
 7. Clerk's Room, University Hall; plaster on wood lath, wood 
 dado; volume, '■2'21 eubie meters; original diu'ation of residual 
 
 I'ui. 11. Ijiborutory. 
 
 sound, 4.10 .seconds; maximum dejiartun- from hyjx'rbola. .10 
 second; average dej)arlure. AH seeoiul.
 
 so 
 
 IJKVKUBKHATION 
 
 S. Faculty-room, I'liiversity Hall; plaster on wood lath, wood 
 dado; voiimu-, 1.480 nihic meters; original duration of residual 
 sound, 7.04 seconds; maximum departure from hyperbola, .18 
 second; average departure, .08 second. 
 
 !». Ix'cture-room, Room 1, Jefferson Physical Laboratory; 
 brick walls, plaster on wood lath ceiling; furnished; volume, 
 1,6;50 cubic meters; original duration of residual sound, 3.91 
 
 Fig. 15. Leclure-room. 
 
 seconds; maximum departure from hyperbola, .10 second; average 
 departure, .04 second. 
 
 10. Large Laboratory, Room 41, Jefferson Physical Laboratory; 
 brick walls, plaster on wood lath ceiling; furnished; volume, 
 1,960 cubic meters; original duration of residual sound, 3.40 seconds; 
 maximum departure from hyiierbola, .03 second; average depar- 
 ture, .01 second. 
 
 11. Lecture-room, Fogg Art ^Luseum; plaster on tile walls, 
 plaster on wire-lath ceiling; volume, 2,740 cubic meters; original 
 duration of residual sound, 5.61 seconds; maximum departure from 
 hyperbola, .04 second; average departure, .02 second. The ex- 
 periments in this room were carried so far that the original duration 
 of residual sound of 5.61 seconds was reduced to .75 second. 
 
 12. Sanders Theatre; plaster on wood lath, but with a great 
 deal of hard-wood sheathing used in the interior finish; volume, 
 9,300 cubic meters; original duration of residual sound, 3.42
 
 APPROXIMATE SOLUTION 
 
 31 
 
 seconds; maximum departure from hyperbola, .07 second; average 
 departure, .02 second. 
 
 It thus appears that the iiyperbolic hiw of inverse proportion- 
 ality holds under extremely diverse conditions in regard to the size, 
 shape and material of the room. And as the cushions used in the 
 calibration were placed about (juite at random, it also apjjears that 
 in rooms small or large, with high or low ceiling, with flat or curved 
 
 Fig. 16. Sanders Theatre. 
 
 walls or ceiling, even in rooms with galleries, the cushions, wherever 
 placed — out from under the gallery, under, or in the gallery — 
 are nearly ec(ually efKcacious as absorbents. This merely means, 
 however, that the efficacy of an absorbent is independent of its 
 position when the problem under consideratii)ii is tliat of reverbera- 
 tion, and that the sound, disjuTsed by regular and irregular reflec- 
 tion and by diffraction, is of nearly the same intensity at all parts of 
 the room soon after the source has ceased; and it will be the object 
 of a .sul)sc(iii(iit i).i]icr l<» show llial in respect to Ihr iiiilial distri- 
 bution of the sound, and also in respect to discrete echoes, the posi- 
 tion of the absorbent is a matter of prime importance.
 
 32 
 
 Ri:vi;i{|{i:i{Ari()\ 
 
 Having shown that tho hyin-rbolii' law is a gi-neral one, interest 
 centers in the parameter, /.-, the constant for any one room, but vary- 
 ing from room lo room, as the following table shows: 
 
 Boom 
 
 1. Comniittcc-rooni, University Hall.. . 
 
 •i. Ijiltorutory, Holanic Gardens 
 
 3. Ortic-e, boUmic Gardens 
 
 4. Recorder's Office 
 
 5. Greenhouse, Botanic Gardens 
 
 C. Dean's Kooin 
 
 7. Clerk's Room 
 
 8. Faculty-room 
 
 9. I<ecture-room, Jefferson Physical Lab- 
 
 oratory, 1 
 
 10. Laboratory, Jefferson Physical Lab- 
 
 oratory, 41 
 
 11. FoKS LiM-tu re-room 
 
 12. Sanders Theatre 
 
 Volume 
 
 65 
 82 
 99 
 
 in-2 
 
 134 
 
 166 
 
 221 
 
 1,480 
 
 1,630 
 
 1,960 
 2,740 
 9,300 
 
 Absorbing Power of 
 Walls, etc., = a 
 
 4.76 
 4.65 
 8.08 
 .5.91 
 5.87 
 7.50 
 10.6 
 34.5 
 
 69.0 
 
 101.0 
 
 75.0 
 
 465.0 
 
 Parameter k 
 
 13.6 
 11.1 
 15.4 
 21.8 
 25.8 
 25.4 
 43.5 
 24.'5.0 
 
 270.0 
 
 345.0 
 
 425.0 
 
 1,590.0 
 
 The values of the absorbing jjower, a, and the parameter, k, are 
 here expressed, not in terms of the cushions actually used in the 
 experiments, l)ut in ti-rms of the o])en-window units, sliown to be 
 preferable in the preceding article. 
 
 In the diagram. Figure 17, the values of A' are plotted against the 
 corresponding volumes of the rooms; here again three different 
 scales are employed in order to magnify the results obtained in the 
 smaller rooms. The resulting straight line shows that the value of 
 /,■ is proportional to the volume of the room, and it is to be observed 
 that the hirgest room was nearly one hundred and fifty times larger 
 than the smallest. By measurements of the coordinates of the line, 
 
 or by averaging the results found in calculating ~ for all the rooms 
 
 it appears that J: = .171 F. The physical significance of this nu- 
 merical magnitude .171 will be exjjlained later. 
 
 This simple relationship between the value of k and the volume 
 of the room — the rooms tested varying so greatly in size and 
 shape — affords additional proof, by a rather delicate test, of the 
 accuracy of the method of experimenting, for it show\s that the ex-
 
 APPROXIMATE SOLUTION 
 
 33 
 
 perimentally dettTmined curvos iijjproxiinate not merely to hyper- 
 bolas but to a .systematic family of hyperbolas. It also furnishes a 
 more pleasing prospect, for the laljorious handling of cushions will 
 be unnecessary. A single experiment in a room and a knowledge of 
 the volume of the room will furnish sufficient data for the calcula- 
 tion of the absorbing powi'r of its coinixjuents. Conversely, a 
 knowledge of the volume of a room and of the coefficients of absorp- 
 tion of its various components, including the audience for which it 
 is designed, will enable one to calculate in advance of construction 
 the duration of audibility of the residual sound, which measures 
 
 u 
 
 IM 
 
 
 
 
 
 
 
 
 
 
 »11 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 9O00 " 
 
 11^0 
 
 12600 
 
 i-T 
 
 i: 100 
 
 
 
 
 
 lOj/ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 yi 
 
 
 
 
 
 
 
 
 
 
 H so 
 
 
 
 
 / 
 
 tzoo 
 
 1800 2400 3000 
 
 1600 
 
 4S00 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 /i 
 
 6/ 
 
 y6 
 
 
 
 
 
 
 
 
 
 
 ■ 
 
 
 
 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 DO 
 
 4( 
 
 M 
 
 6( 
 
 >0 
 
 oluii 
 
 8( 
 
 IPS r 
 
 )0 
 
 f ro 
 
 10 
 
 iins 
 
 «0 
 
 u 
 
 00 
 
 14 
 
 m 
 
 Fit;. 17. The parameter, t, plotted again.st tlic volumes of the 
 rooms, showing the two proportional. 
 
 that acoustical property of a room commonly called reverberation. 
 Therefore, tliis [)li;isc of the problem is solved to a first approxi- 
 mation. 
 
 The fXi)Iaiialion of llic fact that /,• is propoii ioiial to \ is fouiul 
 ill the following rciusoning. Consider two rooms, constructed ot 
 exactly the same materials, similar in relative proportions, but one 
 larger than the other. The rooms being eiiii)ty, .r, the absorbing 
 l)ower of the contained material, is zero, and we liave «' \' = /."' 
 and n" l" = /.•". Since the rooms are con.structcd of I he same 
 iiialcrials the coclliciriits of alooi |)l ioii arc iln' >aiiic, >o llial (/' and 
 r/"are pr()])ortioiial to the .surfaces of llie rooms, that is, to the .•M|Uares
 
 34 REMCRBERATION 
 
 (if tin- linear dimensions. Also, the residual sound is diminished a 
 certain pereentage at eadi reflection, and the more frequent these 
 refleetions are the shorter is the thiration of its audibihly; wlience 
 /' and /" are inversely proi)ortional to the frequency of the reflec- 
 tions, and luiice directly proportional to tlu- linear dimensions. 
 Therefore, A"' and A", which are equal to a' t' and a" t", are propor- 
 tional to the cuIh's of the linear dimensions, and hence to the 
 volumes of the rooms. 
 
 Further, when the shape of the room varies, the volume remain- 
 ing the same, the number of reflections per second will vary. There- 
 fore, A- is a function not merely of the volume, but also of tlie shape 
 of the room. But that it is only a slightly varying function, com- 
 paratively, of the shape of the room for practical cases, is shown by 
 the fact that the points fall so near the straight line that averages 
 
 the values of the ratio — • 
 
 The value of A- is also a function of the initial intensity of the 
 sound; but the consideration of this element will be taken up in a 
 following paper. 
 
 RATE OF DECAY OF RESIDUAL SOUND 
 
 In a subsequent discussion of the interference of sound it w'ill be 
 shown by photographs that the residual sound at any one point 
 in the room as it dies away passes through maxima and minima, 
 in many cases beginning to rise in intensity immediately after the 
 source has ceased; and that these maxima and minima succeed 
 each other in a far from simple manner as the interference system 
 shifts. On this account it is quite impossible to use any of the nu- 
 merous direct methods of measuring sound in experiments on rever- 
 beration. Or, rather, if such methods were used the results would 
 be a mass of data extremely diflicult to interpret. It was for this 
 reason that attempts in this direction were abandoned early in the 
 investigation, and the method already described adopted. In 
 addition to the fact that this method only is feasible, it has the 
 advantage of making the measurements directly in terms of those 
 units with which one is here concerned ^ — the minimum audible
 
 RATE OF DECAY OF RESIDUAL SOUND 
 
 35 
 
 intensity. It is now proposed to extend tliis method to the deter- 
 mination of tlie rate of decay of the average intensity of sound in 
 the room, and to the determination of the intensity of the initial 
 sound, and thence to the determination of tlie mean free path be- 
 tween reflections, — all in i)reparation for tlie more exact solution 
 of the problem. 
 
 The first careful experiment on the absolute rate of decay was 
 in the lecture-room of the Boston Public Library, a large room. 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 a 
 
 3 . 
 
 
 \ 
 
 
 \, 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ ° 
 
 s. 
 
 
 \ 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 >4 
 
 \ 
 
 \, 
 
 
 V 
 
 s 
 
 \ 
 
 S' 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 V 
 
 
 'V 
 
 \ 
 
 
 
 
 
 
 
 
 a 
 
 
 
 
 
 "-- 
 
 
 •■-^ 
 
 
 N^ 
 
 
 
 MUM 
 
 UDIBl 
 
 1 IKTt 
 
 l«IT» 
 
 
 
 "~- 
 
 --. 
 
 — , 
 
 
 
 ■--. 
 
 -i- 
 
 
 ■-»-. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -H-' 
 
 
 
 ---- 
 
 -.- 
 
 
 
 8.5 8.6 8.T 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.* 9.T 9.8 9.9 10. 
 
 Time in seconds 
 
 Fig. 18. Decay of sound in the lecture-room of the Boston Public 
 Library from the initial sound of one, two, three, and four organ 
 pipes, showing only the last second. 
 
 fini.shed, with the exception of the platform, in material of very 
 slight absorbing power — tile ceiling, plaster on tile walls, and 
 polished cement floor.' The reverl)eration was very great, 8.6!) 
 seconds. On the platform were placed foin- organ pipes, all of the 
 same pitch, each on its own tank or wind suj)ply, and each having 
 its own electro-pneumatic valve. All these valves, however, were 
 connected to one chronograph, key, and battery, so that one, two, 
 three, or all the pipes, might be started and stopped at once, and 
 when less than four were in use any desired combination could l)e 
 made. One pipe was sounded and the duration of audibilily nf llu- 
 residual soinid determined, of ctmrse, as always in these expi-ri- 
 ments, by rei)eated olxser vat ions. The ex[ieriment wa,-^ then niade 
 
 ' Terrazzo cement (liK)r.
 
 86 REVERBERATION 
 
 wilh two organ pipes instciid of one; then with three pipes; and, 
 finally, witli four. The whole series was then repeated, but begin- 
 ninj; with a different i)ipe and eonibining different pipes for the two 
 and three pipe sets. In this way the series was repeated four times, 
 the combinations being so made that each pipe was given an equal 
 weight in the determination of the duration of audibility of the 
 residual soiuid under the four ditl'erent conditions. It is safe to 
 assume that with experiments conducted in this manner the average 
 initial intensities of the sound with one, two, three, and four pipes 
 were to each other as one, two, three and four. The corresponding 
 durations of audibility shall be called /i, U, fs and /4. The following 
 results weri' obtained: 
 
 (i = 8.69 seconds h - h = .45 second 
 
 /, = 9.14 " h-h = .67 " 
 
 /, = 9.36 " tt-i, = .86 " 
 
 U = 9.55 " 
 
 It is first to be observed that the difference for one and two organ 
 pipes, .45, is, within two-hundredths of a second, half that for one 
 and four organ pipes, .8(5. This suggests that the difference is 
 proportional to the logarithm of the initial intensity; and further 
 inspection shows that the intermediate result with three organ 
 pipes, .67, is even more nearly, in fact well within a hundredth of 
 a second, proportional to the logarithm of three. This reenforces 
 the very natural conception that however much the residual sound 
 at any one point in the room may fluctuate, passing through max- 
 ima and minima, the average intensity of sound in the room dies 
 away logarithmically. Thus, if one plots the last part of the residual 
 sound — that which remains after eight seconds have elapsed — 
 on the assumption that the intensity of the sound at any instant is 
 proportional to the initial intensity, the result will be as shown in 
 the diagram. Fig. 18. The point at which the diminishing sound 
 crosses the line of minimum audibility in each of the four cases is 
 known, the corresponding ordinates of the other curves being 
 multiples or submultiples in proportion to the initial intensity. 
 The results are obviously logarithmic. 
 
 Let 7i be the average intensity of the steady sound in the room 
 when the single organ pipe is sounding, i the intensity at any instant
 
 RATE OF DECAY OF RESIDTAL SOUND 37 
 
 during the decay, say t seconds after the pipe has ceased, then 
 
 di 
 
 will be the rate of decav of the sound, and since tlie absorption 
 
 dt ' ' 
 
 of sound is proportional to the intensity 
 
 di 
 — — = Ai, where .1 is the constant of proportionality, 
 dt 
 
 the ratio of the rate of decay of the residual sound to the intensity 
 at the instant. 
 
 — loge i + C = At, 
 
 a result that is in accord with the above experiments. The con- 
 stant of integration C may be determined by the fact that when / is 
 zero i is equal to h; whence 
 
 C = fo(/e /], and the above equation becomes 
 log a -7 = At. 
 
 At tlie instant of minimum audibility t is equal to /i, the wliole 
 duration of (lie residual sound, and i is equal to i', — as the inten- 
 sity of the least audible sound will hereafter be denoted. Therefore 
 
 We t] = At 
 
 I 
 
 This apiilieil to tlie experiment with two, three and four pipes gives 
 similar equations of the form 
 
 We -~ = At„, 
 where /; is the number of organ pipes in use. By the elimination of 
 ., from tlicse e(|uati()iis by i)airing the first willi lach of tlic olliers, 
 
 A 
 
 We 
 
 '2- 
 
 i _ 
 
 tx ~ 
 
 1.54, 
 
 A 
 
 log„ 
 ti- 
 
 ti ~ 
 
 1.6^2, 
 
 A 
 
 loge 
 
 tt- 
 
 4 _ 
 
 l.(il. 
 
 -1 (average) = 1.59, 
 
 where A is the ratio between the rate of decay and the average 
 intensity at any instant.
 
 3S 
 
 RKVKUHKRATIOX 
 
 It is j)ossil)K' also ti) tli'tcriniiic the initial intensity. It, in terms 
 of llie luininiiiin iiiulil)le intensity, ('. 
 
 log^ .J = Ah, 
 
 h = i' logi^ Ati = i' log;^ (1.59 X 8.69) = 1,000,000 i'. 
 
 Witli tliis value of the initial intensity it is possible to calculate 
 the intensity i of the residual sound at any instant during the decay, 
 l.y the formula %,/,-%„/ = .K, 
 
 and the result when plotted is shown in Figure 19, the unit of in- 
 tensity being minimum audibility. 
 
 A practical trial early in tiie year liad sliown tiiat it would be 
 impossible to use tin's lecture-room as an auditorium, and the ex- 
 
 1000,000 ; • 
 
 A 
 
 900,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 800,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 700,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ■ 1 
 600,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 l500,00( 
 
 ) 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \400,0( 
 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 300,000 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 
 \ 
 
 200,X>00 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \lOO,00( 
 
 ) 
 
 
 
 
 
 O 
 
 
 
 
 
 
 
 
 ^-J-_ 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 1 
 
 2 
 
 3 ' 
 
 1 ! 
 
 > 
 
 ' 
 
 r i 
 
 1 9 
 
 1 
 
 1 
 
 1 1 
 
 2 t 
 
 3"'l 
 
 1 19 
 
 Time in seconds 
 Fio. 19. Decay of sound in the lecture-room of the Boston Public 
 Library beginning immediately after the cessation of one organ 
 pipe. 
 
 periments described above, with others, were in anticipation of 
 changes designed to remedy the difficulty. Hair felt, in consider- 
 al)le quantities, was placed on the rear wall. The experiments with 
 the four organ pipes were then repeated and the following results 
 were obtained : 
 
 /, = 3.65 k- h = M :. A = 3.41 
 
 h = 3.85 h ~h = .31 .-. A = 3.54 
 
 h = 3.96 U-h = .42 .-. A = 3.29 
 
 /< = 4.07 
 h = 250,000 i' 
 
 A = 3.41 (average)
 
 RATE OF DECAY OF RESIDUAL SOUND 39 
 
 A few nights later the apparatus was moved down to the attend- 
 ant's reception-room near the main entrance — a small room but 
 similar in i)roportions to tlie lecture-room. Here a careful experi- 
 ment extending over several nights was carried on, and it gave the 
 following results: 
 
 U = 4.01 t, ~ ti = .19 .-. A = 3.65 
 
 /2 = 4.'-20 t, - ti = .28 .-. A = 3.90 
 
 /3 = •l.'JO ti- li = .37 .-. A = 3.75 
 
 U = 4.38 A = 3.76 (average) 
 
 /i = 3,800,000 i' 
 
 The first interest lies in an attempt to connect the rate of decay, 
 obtained by means of the four organ pipe experiments, with the 
 absolute coefficient of absorption of the walls, obtained by the 
 experiments with the open and closed windows; and to this end 
 recourse will be had to what shall here be called "the mean free 
 path betwet'u reflec-tions." The residual sound in its i)rocess of 
 decay travels across the room from wall to wall, or ceiling, or floor, 
 in all conceivable directions; some paths are the whole length of 
 the room, some even longer, from one corner to the opposite, but 
 in the main the free path between reflections is less, becoming even 
 infinitesimally small at an angle or a corner. Between the two or 
 three hundred reflections that occur during its audibility the residual 
 sound establishes an average distance between reflections that de- 
 pends merely on the dimensions of the room, and nuiy be called 
 "its mean free path." 
 
 .171 r 
 
 is the absorbing power of the room, measured in open-window units. 
 Let 
 
 « = surface. 
 
 V = volume. 
 
 A = rate of decay of tlie soinui. 
 
 V = velocity of sound, '.U-^i in. per second at 20 degrees C. 
 p = length of the mean free path httweea reflections. 
 
 Whence = the average number of reflect ion> i)er second, and 
 P 
 
 - is the fraction absorbed at each reflection, = •'■
 
 40 
 
 REVEnBERATIOX 
 
 ar r.l71 l . 11,1,1 *■ 
 
 and P = T = — r~r' whencr inav be calcuhiU'd the mean tree 
 ,1s .1.'' /i 
 
 patli, p. 
 
 Boston Public Library Lecture-room, bare 2,140.0 1.59 1,160 8.69 7.8 
 
 with felt .. 2,140.0 3.41 l.lfiO 3.0.5 8.8 
 .\llentlanfs Room 63.8 3.76 108 4.01 2.27 
 
 The lenpth of the mean free path in the lecture-room, bare or 
 draped, ouglit to l)e the same, for the felt was placed out from 
 the wall at a distance imperceptibly small in comparison with the 
 dimensions of the room: l)nt 7.8 and 8.8 differ more than the 
 experimental errors justify. Again, the attendant's room had very 
 nearly the same relative proportions as the lecture-room (about 
 2 :3 -.6), but each linear dimension reduced in the ratio 3.22 : 1. 
 Tiie mean free path, obviously, should be in the same ratio; but 
 when the mean free path in the attendant's room, 2.27, is multiplied 
 by 3.22 it gives 7.35, departing again from the other values, 7.8 and 
 8.8, more than experimental errors justify. The explanation of 
 this is to be found in the fact that the initial intensity of the sound 
 in the rooms for the determination of /i was not the same but had 
 the values respectively, 1,000,000 i', 250,000 i' and 3,800,000 i'. 
 Since ti has been shown proportional to the logarithms of the initial 
 intensities, these three numbers, 7.8, 8.8 and 7.35, may be corrected 
 in an obvious manner, and reduced to the comparable values they 
 would have had if the initial intensity had been the same in all 
 three cases. The results of this reduction are 7.8, 8.0 and 8.0, a 
 satisfactory agreement . 
 
 The length of the mean free path is, therefore, as was to be ex- 
 pected, proportional to the linear dimensions of the room, and such 
 a comparison is interesting. There is no more reason, however, for 
 comparing it with one dimension than another. Moreover, most 
 rooms in regard to which the inquiry might be made are too irregular 
 in shape to admit of any one actnal distance being taken as standard. 
 Thus, in a semicircular room, still more in a horseshoe-shaped room 
 such as the common theatre, it is indeterminable what should be
 
 RATE OF DECAY f)F RKSIDrAL SOrXD 41 
 
 called the breadth or what the length. On account, therefore, of 
 the complicated nature of practical conditions one is forced to the 
 adoption of an ideal dimension, the cube root of liie volume, f ■\ tlie 
 length of one side of a cubical room of the same capacity. The above 
 
 data give as the ratio of the value, .62. 
 
 It now becomes possible to present the subject by exact analysis, 
 and free from approximations; but before doing so it will be well to 
 review from this new standpoint that which has already been done. 
 
 It was obvious from the beginning, even in deducing the hyper- 
 bolic law, that some account should be taken of tiie rethiclion in 
 the initial intensity of the sound as more and more absorbing 
 material was brought into the room, even when the source of sound 
 remained unchanged. Thus each succeeding value of the duration 
 of the residual sound was less as more and more absorbing material 
 was brought into the room, not merely because the rate of decay 
 w:is greater, but also because the initial intensity was less. Had the 
 initial intensity in some way been kept up to the same value through- 
 out the series, the resulting curve would have been an exact liyper- 
 bola. As it was, however, the curve sloped a little more rapitlly on 
 account of the additional reduction in the duration arising from the 
 reduction in initial intensity of the sound. At the time, there was 
 no way to make allowance for this. That it was a very small error, 
 however, is shown bj' the fact that the departures from the true 
 hyperbola that were tabulated are so small. 
 
 Turning now lo the i)arameter, k, it is evident lliat this also was 
 an approximation, though a close one. In the first place, iis just 
 explained, the experimental curve of calibration sloped a little more 
 rapidly than tlie tr\ie iiy])erbola. It follows that the nearest hyper- 
 bola fitting the actual experimental results was always of a little 
 too MiKill parameter. Eurtlier, /.• depended iiol uurcly mi llic uni- 
 formity of the initial intensity during the (•alil)ration of the room, 
 but also on the a1)solute value of tliis intensity. Tluis, /,• = ati, ami 
 ti is in turn proportional to llic logarithm of tlic initial intensity. 
 Therefore in order to fully define h we must adopt some standard of 
 initial intensity. For this purpose we shall hereafter take as the
 
 42 RKVKHHKUATIOX 
 
 sUindard coiulition in initial intensity, / = 1,000,000 i', (/ = 10® i'), 
 wluTi- ?■' is tlu- niiniinuni aiidihle intensity, as this is the nearest 
 round number to the average intensity prevailing during these ex- 
 periments. If, therefore, during the preceding experiments the 
 initial intensity was above the standard, the value deduced for k 
 would be a little high, if below standard, a little low. This variation 
 of the parameter. Ic, would be slight ordinarily, for k is proportional 
 to the logarithm, not directly to the value of the initial intensity. 
 Slight ordinarily, but not always. Attention was first directed to 
 its practical importance early in the whole investigation by an ex- 
 periment in the dining-room of Memorial Hall — a very large room 
 of 17,(HK) c iil)ic meters capacity. During some experiments in Sanders 
 Theatre the organ pipe was moved across to this dining-room, and 
 an experiment begun. The reverberation was of very short duration, 
 although it would have been long had the initial intensity been 
 standard, for in rooms constructed of similar materials the rever- 
 beration is approximately proportional to the cube roots of the 
 \ohunes. There was no opportunitj' to carry the experiment farther 
 than to observe the fact that the duration was surprisingly short, 
 for the frightened apjiearance of the women from the sleeping- 
 rooms at the top of the hall put an end to the experiment. Finally, 
 fc is a function not merely of the volume but also of the shape of the 
 room; that is to say, of the mean free path, as has already been 
 explained. 
 
 It wius early recognized that with a constant source the average 
 intensity of the sound in different rooms varies with variations in 
 size and construction, and that proper allowance should be made 
 therefor. The above results call renewed attention to this, and 
 point the way. In the following paper the more exact analysis will 
 be given and applied.
 
 EXACT SOLUTION 43 
 
 EXACT SOLUTION 
 
 The present paper will carry forward the more exact analysis pro- 
 posed in the hist i)aper. 
 
 For the sake of reference the nomenclature so far introduced is 
 here tabulated. 
 
 t = lime after the source has ceased up to any instant whatever liuring 
 
 the decay of the sound. 
 
 /', t", t'" = (hiration of the residual sound, the accents indicating a changed 
 
 condition in the room sucii as tlie intnxhiction or removal of 
 some al)Sorlient, the presence of an au<iien<'e, or the opening of 
 a window. 
 
 h, hi • ■ ■ ta = whole duration of the residual .sound, the subscripts indicating the 
 nnniher of organ [lipes used. 
 
 T = <luration of the resi<lual sound in a room when the initial intensity 
 
 has been standard. 
 
 i = intensity of the residual .sound at any instant. 
 
 i' = intensity of minimum audil>ility. 
 
 I\, Ii, . . . I„ = intensity of sound in the room just as the organ pipe or pipes stop, 
 the subscripts indicating number of [)ipes. 
 
 I = standard initial Intensity arbitrarily adopted, / = 1,000,000 i'. 
 
 W = absorbing power of the oi)cn windows, minus their ab.sorlting 
 
 power when closed = area (1 — .024). 
 
 a = ab.sorbing power of the room. 
 
 Oi, 02, . . . a,i = coefficients of absorption of the various components of the wall- 
 surface. 
 
 S = area of wall (and floor) surface in square meters. 
 
 *i, S2, . . . *n = area of the various comi)onents of the wall-surface. 
 
 V = volume of the room in cubic meters. 
 k = hyperbdlic parameter of any room. 
 
 K = ratio of the parameter to the volume. aT = k = KV. 
 
 A = rate of decay of tlie sound. 
 
 p = length of mean free path between reflections. 
 
 V = velocity of sound, 3-J'2 m. per second at 20° C. 
 
 Let E denote Die rate of emission of energy from the single 
 organ pipe. 
 
 ^ = the average interval of time between reflections. 
 
 -E = aiiioiiiil of eiiergv eniilted during' tliis iiiUrval. 
 
 V 
 
 ^ e(i —") = amount of energy left after I he first reflection. 
 
 V E (\ -") = amount of energy left after the second reflection, etc.
 
 H HKVKUnKHATIOX 
 
 If I lit- iirj,';in pii"' contimu-s to sound, the energy in the room con- 
 timifs to acciiimilate, at first rapidly, afterwards more and more 
 slowly, and finally reaches a practically steady condition. Two 
 |)oints are here interesting, — the time reciuind lor llie sound to 
 reach a practically steady condition (for in tlie experiments the 
 organ pipes ought to he sounded at least this long), aiul second, the 
 intensity of the sound in the steady and final contlition. At any 
 instant, the total energy in the room is that of the sound just issuing 
 from till' ]>ii)e. Mot having suffered any reflection, plus the energy of 
 that which Inus suffered one reflection, that which has suffered two, 
 that which has suffered three, and so on hack to that which first 
 issueil from the pipe, as: 
 
 where n is the number of reflections suffered by the sound that first 
 issued from the pipe, and is equal to the length of time the i)ipe was 
 blown divided by the average interval of time between reflections. 
 The above series, which is an ordinary geometric progression, may 
 be written 
 
 ?£ )-^ : m 
 
 (>-:) 
 
 is by nature positive and less than unity. If /; is very large or if 
 is small this may be written 
 
 - — = the total energy in the room in the steadv condition. (2) 
 va . V / 
 
 i^ = ^; (3) 
 
 avV ^ ' 
 
 is the average intensity of soimd in the room as the organ pipe 
 stops. Substituting in this equation the values of a and p already 
 found, 
 
 « = ^ ' (4) 
 
 va vKV
 
 EXACT SOLUTION 45 
 
 J vKV T Es E 
 wehave ^' = Sat' KV' ^ = M'' ^^^ 
 
 Also 
 whence 
 
 /. = log? Ah. (7) 
 
 /: = (-.f /or/-- .1/,, (8) 
 
 wlitTf the unit of enorgy is the energy of niininiuni audibility in a 
 cubic meter of air. 
 
 It remains to determine A' and a. To this end the four organ 
 pipe experiments must be nuide in a room with the windows closed 
 and with them open, and the values of A' and A" deternu'ned. The 
 following analysis then becomes available: 
 
 AT , , KV 
 
 a = y, , and a + w = ^ - 
 
 whence 
 
 a + w T ' 
 
 For >lan<!aril conditions in regard to initial intensity 
 
 A' r = A" T" = lag, I = log, (lO-^) = 13.8, 
 
 r A' , ^, 13.8 
 
 j;r = ^.andr =-^. 
 
 Substituting these values, 
 
 a A' ,. al" a 13.8 
 
 :. A = 
 
 a + w A"' V A'V 
 
 whence 
 
 and 
 
 
 •^'YW^y « 
 
 Or if A lias been determined (!)) nuiy l)e written 
 
 « = •''>''-. (11) 
 
 13.8 
 
 a useful form of the equation. 
 
 From equation (1) and ('■2) we may calculate the rate of growth 
 of soiuid in tlie room as it approaches the final steady c*>ndition.
 
 46 KK\KUBERATION 
 
 Thus, dividing (1) by (2), the result, 1 - (l - ^)°, gives the in- 
 
 tt-nsitv at aiiv instant h? seconds after the sound has started, in 
 
 terms of the final steady intensity. Of all the rooms so far experi- 
 mented on, liie growth of the sound was slowest in the lecture-room 
 of the Boston Public Library in its unfurnished condition. For this 
 
 room - = .037, and p = 8.0 meters. The following table shows the 
 
 growth of the sound in this room, and the corresponding number of 
 reflections which the sound that first issued from the pipe had 
 undergone. 
 
 Lecture-koom. Boston Public Libhauy 
 
 II 
 
 Time 
 
 Average 
 Intensity 
 
 n 
 
 'nnw 
 
 Average 
 Intensity 
 
 1 
 
 .02 
 
 .04 
 
 30 
 
 .69 
 
 .08 
 
 5 
 
 .11 
 
 .17 
 
 40 
 
 .92 
 
 .78 
 
 10 
 
 .23 
 
 .31 
 
 50 
 
 1.15 
 
 .85 
 
 15 
 
 .84 
 
 .43 
 
 100 
 
 2.30 
 
 .98 
 
 20 
 
 .46 
 
 .53 
 
 150 
 
 3.45 
 
 .997 
 
 00 
 
 00 
 
 1.00 
 
 It thus appears that in this particular room the organ pipe must 
 sound for about three seconds in order that the average intensity 
 of the sound may get within ninety-nine per cent of its final steady 
 value. As throughout this work we are concerned only with the 
 logarithm of the initial intensity, ninety-nine per cent of the steady 
 condition is abundantly near. Tliis consideration — the necessary 
 length of time the organ pipe should sound — is carefully regarded 
 throughout these experiments. It varies from room to room, being 
 greater in large rooms, and k-ss in rooms of great absorbing power. 
 
 To determine the value of E, the rate of emission of sound by 
 the pipe, formula (8), E = VA logP Ah, is available. It is here to 
 be observed that as this involves the antilogarithm of Ati these 
 quantities must be determined with the greatest possible accuracy. 
 The first essential to this end is the choice of an appropriate room. 
 Without giving the argument in detail here, it leads to this, that 
 the best rooms in which to experiment are those that are large in 
 volume and have little absorbing power. In fact, for this purpose, 
 small rooms are almost useless, but the accuracy of the result in-
 
 EXACT SOLUTION 47 
 
 creases rapidly with an increase in size or a decrease in absorbing 
 power. On this account the lecture-room of the Boston Public 
 Library in its unfurnished condition was by far the best for this 
 determination of all the available rooms. Inserting the numerical 
 magnitudes obtained in this room in the equation, 
 
 E = VAlogl^Ati = 2,140 X 1.59 logl' {1.59 X 8.69) = 3,400,000,000. 
 
 If the observations in the same room after the introduction of the 
 felt, already referred to, are used in the equation the resulting value 
 of E is 3,200,000,000. The agreement between the two is merely 
 fortunate, for the second conditions were very inferior to the first, 
 and but little reliance should be placed on it. In fact, in both re- 
 sults the second figures, 4 and 2, are doubtful, and the round num- 
 ber, 3,000,000,000, will be used. It is sufficiently accurate. 
 
 The next equation of interest is that giving the value of K, 
 number (10). It contains the expression. A" — A', the difference be- 
 tween the rates of decay with the windows open and witli themclosed; 
 A"iind ^1' depend linearly on the difference in duration of the residual 
 sound with four organ pipes and with one, and jis both sets of dif- 
 ferences are at best small, it is evident that these experiments also 
 must be conducted with the utmost care and under the best con- 
 ditions. The best conditions would be in rooms that are large, that 
 have small absorbing power, and that afford window area sufficient 
 to about double the absorbing power of the room. Practically this 
 would be in large rooms that are of tile, brick, or cement walls, 
 ceiling and floor, and have an available window area equal to about 
 one-fliirlieth of tlie total area. 
 
 The lobby of the Fogg Art Museum, although rather small, best 
 satisfied the desired conditions. Sixteen organ pipes were used, 
 arranged four on each air tank and, Micrefore, near together. Thus 
 arranged, the sixteen i)ipes had 7.0 times the intensity of one, as 
 detennined by a subsequent experiment in the Physical Laboratory. 
 The following results were obtained: 
 
 , ^ tog. 7.6 ^ _Jog,l.6_ ^ 3 Q 
 t\t-t\ 5.26-4.59 
 
 , Af - '"?? "^-^^ - 1 - 
 
 and A "3.43 -3.00 "■*•'•
 
 48 iu;m:hhkhatk)n 
 
 l'3.»w 1:J.8 X 1.8,5 
 
 A = = = .loo. 
 
 V(A' -A') 96 X 1.7 
 
 lien'. liowfVcT, it is t-iisy to sliow by trial that t-rrors of only one- 
 luiiulncllli of a second in the four detorniinations of the duration 
 of the residual sound would, if additive, give a total error of twenty 
 l)er cent in tin- result. 
 
 It is iiii|)ossil)le, es])ecially with open windows, to time with an 
 accuracy of more than one-Jmndredtli of a second, and, therefore, 
 this fornmla, 
 
 13.8«; 
 
 A' = 
 
 ViA" - A') 
 
 while analytically exact and attractive in its simplicity, is practi- 
 cally unserviceable on account of the sensitive manner in which the 
 observations enter into the calculations. 
 
 The following analysis, however, results in an equation much 
 more forbidding in appearance, it is true, but vastly better practi- 
 cally, for it involves the data of difficult determination only logarith- 
 mically, and then only as part of a comparatively small correcting 
 term. For the room with tlie windows closed: 
 A't\ = loy^I'u 
 
 and for standard conditions in regard to initial intensity 
 A' r = log, I, 
 
 whence 
 
 r = v, - :^^iogJ-^- 
 
 T'a = AT, 
 
 hence 
 
 AT =t'ia - j,log^Y'^ 
 
 and similar steps for the same room with the windows open give 
 KV = fi (a -1- it;) - ^--^~ loge -j ■ 
 
 -Mullii)lyiiig the first of the last two equations by t"u and the 
 second by t'l, 
 
 K - 1 [„„/ ,,' , /«'". , 1\ {a + w)t \ , /"A]
 
 EXACT SOLUTION 49 
 
 Bj' equation (5) 
 
 
 a !<p 
 
 Z' " 7 
 
 and similarly 
 
 
 
 a -\- w sp 
 
 
 A" ~ V 
 
 Subslitiiling these values in I he above equation, 
 
 (12) 
 
 As an illustration of the application of the last equation, the 
 case of the lobbyof the Fogg Art ^luseuni is here worked out at 
 length. 
 
 t'l = 4.5!) 
 t'\ = .S.OO 
 F = 96 cii. 111. 
 S = 125 sq. 111. 
 w = 1.8G 
 
 a = - — ; — = 3.58 as a first approximation 
 
 p = 2.8 
 
 /', = 2^ = 8.8 X 106 i' 
 vaV 
 
 /". = , ^\,. = 5.8 X 10« i' 
 
 V (a + w) V 
 
 Substituting these values in the above equation, 
 
 A' = — [25.7 + 1.02 (6.53 - 8.1)1 = .169 - .010 = .159, 
 152 
 
 where the t.eriii .169 is the value of A' that would i)e deduced dis- 
 regarding the initial intensity of the sound, — .010 is the correction 
 for this, and .15!) is llie corrected value of A'. 'Hie magnitude as 
 well as the sign of liiis correction dejieuds on the intensity of the 
 source of sound, the size of the room and the material of which it 
 is constructed, and the area tif the windows opened. This is illus- 
 trated in llie following table, which is derived from a recalculation 
 of all the rooms in which the open-window exiieriment has lieeii 
 tried, and which exliiiiils a fairly large range in these respects:
 
 50 
 
 REVERBERATION 
 
 Boom 
 
 Uncor- 
 rected 
 
 Correc- 
 tion 
 
 I^ihhy Fojig Museum 
 
 Ix>lihv Fork Museum. 10 pipes. . 
 Jefferson I'hysieal I^ahoriitory 15 
 Jefferson I'liysu'iil Lalioratory 1 . 
 Jefferson I'liysieul Lalxirulory 41 
 
 96 
 
 96 
 
 202 
 
 1,630 
 
 1,960 
 
 8,800,000 
 
 67,000,000 
 
 1,700,000 
 
 ;!!)0,000 
 
 300,000 
 
 1.86 
 1.86 
 5.10 
 12.0 
 14.6 
 
 .169 
 .191 
 .164 
 .150 
 .137 
 
 -.010 
 -.027 
 -f.005 
 + .017 
 -f.024 
 
 .159 
 .164 
 .169 
 .167 
 .161 
 
 Average value oi K = .164 
 
 Tlic value, A' = .164, having been adopted, interest next turns 
 to the determination of tlie ab.sorbing power, a, of a room. For this 
 purpose we have clioice of three equations, two of which have 
 already been deduced, (9) and (11), 
 
 a = 
 
 A'w 
 r - A' 
 
 and 
 
 A'KV 
 13.8 
 
 and a third equation may be obtained as follows: 
 It has been shown that 
 
 and 
 
 Therefore 
 
 and 
 
 r = (', - '^ log 
 va 
 
 T'a = KV. 
 
 I\ 
 
 ai\ - "£ log, ^-^ = KV, 
 
 a = l{KV + ^flog.^) 
 
 (13) 
 
 Of these three equations the first, (9), for reasons already pointed 
 out in regard to a similar equation for A', while rigorously correct, 
 yields a result of great uncertainty on account of its sensitiveness 
 to slight errors in the several determinations of the duration of the 
 residual sound. The second, (11), is very much better than the 
 first, but stDl not satisfactory in this respect. The third, (13), is 
 wholly satisfactory. It has the same percentage accuracy as t'l.
 
 EXACT SOLUTION 51 
 
 and the only elements of difficult determination enter logarithmi- 
 cally in a small correcting term. 
 
 As an illustration of the application of these equations we maj' 
 again cite the case of the lobby of the Fogg Art Museum: 
 
 , ,. ,„. 3.0 X 1. 86 „„ 
 
 by equation (9), a = ^ ^ ^ =3.3; 
 
 k f /^l^ 3.0 X .164 X 06 „^ 
 by equation (11), a = —-- = 3.4; 
 
 by equation (13), a = ~ (.164 X 96 + 1.02 X log„ 8.8) = 3.8. 
 4.59 
 
 The first two are approximate only, the last, 3.8, is correct, with 
 
 certainty in regard to the last figure. 
 
 There is but one other subject demanding consideration in this 
 way, — the calculation of the absorbing jiower of object-s lirought 
 into the room, as cushions, drapery, chairs, and other furniture. 
 This may be approached in two ways, either by means of the rate 
 of decay of the sound and the four organ pipe experiment, or by 
 open-window caliliration and a single organ i)ipe. 
 
 Let A'" be the rate of decay when the object is in the room, .1' 
 being the rate when the room is emiity. Then if a' is the absorbing 
 power of the object : 
 
 A'KV 
 
 a = 
 
 and 
 
 Whence 
 
 a -[-a' 
 
 13.8 
 
 A'" KV 
 
 13.8 
 
 «' = (^"'--^'^i^- (u) 
 
 Or from I lie other point of view, f(|ii;iti()ii (13), 
 
 « = ^, ( A' I ■ + — log„ - - 
 /'i \ V I 
 
 whence 
 
 —7.7^ 7 U '"'' 1 - P; '"''• ^i) • (15)
 
 52 REVERBERATION 
 
 where I\ and I"\ are to be calculated as heretofore by a preliminary 
 and approximate estimate of a and a . 
 
 Here also it is easy to show a priori that the first equation, (U), 
 while perfectly correct and analytically rigorous, is excessively 
 sensitive to verj' slight errors of observation, and that on this ac- 
 count equation (15) is decidedly preferable. For example, felt 
 being I)r()iight into the lobby of the Fogg Lecture-room and placed 
 on the floor, the values of A'" and t"\ were determined to be, re- 
 spectively, 4.9 and 2.79. Borrowing from the preceding experiment, 
 and substituting in equations (14) and (15) we have 
 
 „.= («- 3.0) •'«t,f"=«. 
 
 , .164x96(4.59-2.70) ,»,/!, qo ^ i r ^\ o j. 
 
 a = ^^ — 1.0"2 I /of/e8.8 — /r»(7efi-l ) = 2.4, 
 
 4.59X2.79 \4.59 •" 2.7!) '' / 
 
 a very satisfactory agreement in view of the extreme sensitiveness 
 of equation (14). 
 
 Thus three equations have been deduced, number (12) for the 
 calculation of the parameter, k, (13) for the absorbing power, a, of 
 the wall-surface, and (15) for the absorbing power, a', of introduced 
 material. Each has been verified by other equations analytically 
 rigorous, and developed along very different lines of attack. In 
 each case the agreement was satisfactory, especially in view of the 
 extreme sensitiveness of the equations used as checks. 
 
 In the succeeding paper will be deduced, by the method thus 
 established, the coefficients of absorption of the materials that are 
 used ordinarily in the construction and furnishing of an auditoi'ium. 
 
 THE ABSORBING POWER OF AN AUDIENCE, 
 AND OTHER DATA 
 
 Ix this paper will be given all the data ordinarily necessary in 
 calculating the reverberation in any auditorium from its plans and 
 specifications. In order lo show the degree of confidence to which 
 these data are entitled a very brief account will be given of the 
 experiments by means of which they were obtained. Such an ac- 
 count is especially necessarj' in the case of the determmation of the 
 absorbing power of an audience. This coefficient is, in the nature
 
 ABSORBING POWER OF AX AFDIEXCE 53 
 
 of things, a factor of every problem, and in a majority of cases it is 
 one of the most important factors; yet it can be determined only 
 through the courtesy of a large number of persons, and even then 
 is attended with difficulty. 
 
 The formulas that will be used for the calculation of absorbing 
 power are numbers (13) and (15) in the preceding paper, the correct- 
 ing terms being at times of consideral)le importance. Tlie applica- 
 tion of these formulas having been illustrated, the whole discussion 
 here will be devoted to the conditions of the experiments and the 
 results obtained. 
 
 In every experiment the unavoidable presence of the ol)scrver 
 increases the absorl)ing power. In small rooms, and in large rooms 
 if bare of furniture, the relative increase is considerable, and should 
 always be subtracted from the immediate results of the ex-periment 
 in order to determine the absorbing power of the room alont>. The 
 quantity to be sul)tracfed is constant, j)roviile(l the same clot lies 
 are always worn, and may be determined once for all. For this 
 determination another observer made a set of experiments in a Muall 
 and otherwise empty room before and after the writer had entered 
 with a duplicate set of apparatus, — air tank, chronograph, and 
 battery. In fact, two persons made indejiendent observations, 
 giving consistent 1,\- tlie result that the writer, in the clothes and 
 with the api)aratus constantly employed, had an absorbing power 
 of .48 of a imit. For the sake of brevity no further mention will be 
 made of this, but throughout the work this correction is applied 
 wherever necessary. 
 
 In the second paper of lliis series a i)r('liiuinary calculation was 
 made of the absorbing ])()wcr of certain wall-.surfaces, ami I lie ()l)jcct 
 in so doing was to gel an a])])roximate value for the absorbing power 
 of glass. It had been decided that the most convenient unit of 
 absorbing jxiwcr was a sqoiire meter of open window. It is <\ idcnt, 
 however, that the process of oi)ening a window during the progress 
 of an experiment is merely sultstitutiug tlie absorbing power of the 
 open window for thai of the same window closed, — a consitleralion 
 of possililc iiioiiiciil ill I he nicer d<'\<'I(>pnicnl of I hi- >ul>jfcl. 1 liis 
 preliminary calculation wa-> in anticipation of and preparation for 
 the more close analysis in llir fiflli pa|>ir. If tlicse cocflicients are
 
 54 RKVKHBKRATIOX 
 
 now calculated, using the corrected formulas of the fifth paper, we 
 arrivf at llu- following results: Cement, and brick set in cement, 
 .(h».'>, ^'la>s. .(►•27 and wood sheathing, .061. 
 
 TIk- experinients in the Boston Public Library gave results that 
 ju-e interesting from several points of view. The total absorbing 
 power of the large lecture-room was found to be 38.9 units dis- 
 tributed :us follows: A platform of pine sheathing, exposing a total 
 area of 70 squjire meters, had an absorbing power of 70 X .001=4.3; 
 7(2 square meters of glass windows had an absorbing power of 
 7-2 X .0*27 = 1.9; three large oil paintings, with a total area of 17.4 
 square meters, had an absorbing jjower of 17.4 X .'iS = 4.9; the 
 remainder, "27.8 units, was that of the cement floor, tile ceiling, and 
 phuster on tile walls, in total area 1,095 square meters. This gives 
 as the coefficient of absorption for such construction .0254. A 
 similar calculation of results obtained in the attendant's room in 
 the same building — a room in which the construction of the floor, 
 walls, and ceiling is similar to that in the lecture-room — gives for 
 the value of the coeflScient, .0255. The very close agreement of 
 these results, and their agreement witli tlie coefficient, .0251, for 
 cement floor and solid walls of brick set in cement in the constant- 
 temperature room, is satisfactory. However, a far more interest- 
 ing consideration is the following: 
 
 Heretofore in the argument it has been assumed, tacitly, that 
 the total absorption of sound in a room is due to the walls, furniture 
 and audience. There is one other possible absorbent, and only one 
 — the viscosity of the vibrating air. It is now i>ossible to present 
 the argument that led to the conclusion that this, the viscosity of 
 the air throughout the body of the room, is entirely negligible in 
 comparison with the other sources of absorption. These two rooms 
 in the Boston Public Library — the lecture-room and the attend- 
 ant's room — had, in their bare and unfurnished condition, less 
 absorbing power in the walls than any other rooms of their size yet 
 found. Therefore, if the viscosity of the air is a practical factor it 
 ought to have shown in these two rooms if ever. Fortunately, also, 
 the two rooms differed greatly in size, the volume of one being about 
 thirty-five times that of the other, while the ratio of the areas of 
 the wall-surfaces was about twelve. That part of the absorption
 
 ABSORBINCJ POWER OF AN AUDIENCE 55 
 
 due to the walls \vtu> proportional to the areas of the walls, and the 
 part due to the viscosity of the air was proportional to the volumes 
 of the rooms. As a matter of fact the experiments in these two 
 rooms showed that the whole absorbing power was accurately pro- 
 portional to the areas of the walls; how accurately is abundantly 
 e\itienced by the agreement of the two coefficients, .0^254 and AHoa, 
 deduced on the supposition that the viscosity of the air was negli- 
 gible. To express it more precisely, had the viscosity of the air 
 been sufficient to produce one-fiftieth part of the absorption in the 
 attendant's room, these two coetlicients would have differed from 
 each other by four per cent, an easily measurable amount. It is safe 
 to conclude that in rooms as bare and nonabsorbent as these the 
 viscosity of the air is inconsiderable, and that in a room filled with 
 an audience it is certainly wholly negligible. Rooms more suitable 
 for the demonstration of this ])oint than these two rooms in the 
 Boston Public Library could hardly be designed, and access to them 
 was good fortune in settling so directly and conclusively this funda- 
 mental ((uestion. 
 
 The experiments to determine the ul)sorbing power of plastered 
 walls show it to be variable. If the plaster is applied directly to 
 tile or luick the absorbing power of the resulting solid wall is uni- 
 formly .0'25. But if the plaster is ai)i)lied to lath held out from the 
 solid wail by studding, the absorbing i)ower is not nearly so constant, 
 varying in difiVrent rooms. The investigation of this has not been 
 carried far enough to show witli absolute certainty the cause, al- 
 though it probabh' arises from the different thickness in which the 
 l)laster is applied. For the examination of this point two modes of 
 procedure are ])ossible, — experimenting in a large number of 
 rooms, or experimenting in one room and replastering in many 
 different ways. The objection to the first nietliod, which appears 
 the more available, is that it is almost imi)ossible to get accurate 
 information in regard to the nature of a wall unless one hivs comjilete 
 cuiilrol of tiie construction. However, there are probably interest- 
 ing variations that cannot be found in u>f, l)ut that, if tried, would 
 be fruitful in suggestions for future conslruclion. The second 
 method - experimenting in one room, ])lastering and replastering 
 it with svslemalic variations antl careful analysis of the construction
 
 56 RK\KI?I?l-:RA'ri()\ 
 
 in oacli ciise — would be the most instructive, but the expense of 
 such proccihirc is, for the time bcin^' at least, prohibitive. Ainon^ 
 the interesting possibilities, of which it can only be said that the 
 experiments so fur point that way, is that with time the plastered 
 walls improve in absorbing power; how rapidly has not been shown, 
 'lln's change can be due, of course, only to some real cliange in the 
 nature of the wall, and the most probable change would l>e its grad- 
 ual drying out. Experiments in four rooms with plaster on wood 
 lath gave as the average absorbing power per scpiare meter .034 of 
 a unit. Experiments in eight rooms with plaster on wire lath gave 
 as the average coefficient of a!)sorption .0.'5.'3. In both cases the 
 variation among the tliH'erent rooms was such that the figure in the 
 third decimal place may be greater or less by three, possibly, though 
 not probabl\". l)y more. The fact that a considerable pari of tlie 
 wall-surface of several of the rooms was of uncertain construction 
 is partly responsible for this uncertainty in regard to the coefficient. 
 For the sake of easy reference and comparison the.se results are 
 tabulated, the unit being the absorbing power of a square meter of 
 open-window area. 
 
 Absorbing Power of Wall-Surfaces 
 
 Open window 1.000 
 
 Wood-shoatliing (hard pine) 061 
 
 riastiT on wood iatli 034 
 
 Piaster on wire latii 033 
 
 (ilass, siiifile ihiekness 027 
 
 I'iaster on tile 025 
 
 Brick set in Pcirllaml icmcnl 025 
 
 Next in interest to the al)sorbing ])ower of wall-surfaces is that 
 of an audience. During the smnmer of 1897, at the close of a lecture 
 in the Fogg Art Museum, the duration of the residual soimd was 
 determined l)efore and innnediately after the audience left. The 
 patience of the audience and the silence preserved left nothing to 
 be desired in this direction, but a slight rain falling on the roof 
 .seriously interfered with the observations. Nevertheless, the result, 
 .87 per jjcrson, is worthy of record. The experiment was tried again 
 in the summer of 1899, on a much more elaborate scale and under 
 the most favorable conditions, in the large lecture-room of the 
 Jefiferson Physical Laboratory. In order to get as much data and
 
 ABSORBING POWER OF AX AUDIENCE 
 
 ot 
 
 from ;is iiuk'perKk'nl sources as possil)It', tliree chrom'^riij)lis were 
 ek'clrifully connected willi each other and with the electro-pneu- 
 matic valve controUing the air supply of the organ pipe. One 
 chronograph was on the Icclurc-lalilc, and the others were on op- 
 posite sides in the rear of the hall. The one on the table was in 
 charge of the writer, who also controlled the key turning on and ott" 
 the current at the foiu" instnunenls. The two other chnjuographs 
 were in charge of ullicr ohservers. ])r()visi()n heing thus made for 
 three independent determinations. After a test had been made of 
 the absorbing jjower of the whole audience — 157 women and i;?5 
 men, sufficient to crowd the lecture-room — one-half, by request, 
 passed out, 63 women and 79 men remaining, and observations 
 were again made. On the following night the lecture was repeated 
 and ol)servations were again taken, there lieing present 95 women 
 and 13 men. There were thus six independent determinations on 
 three different audiences, and by three observers. In the following 
 table I he lirsl cohiiiui ol' figures gi\-('s the t(jlal absorbing ])ower of 
 the audience present; the second gives the absorbing jjower pw 
 person; the initials indicate the observer. 
 
 
 Observer 
 
 Total Absorbing 
 Power 
 
 .\hsorbinK Power 
 iwr Person 
 
 First night 
 
 whole aud 
 
 ience 
 
 w. c. s. 
 
 H.S.O 
 
 .42 
 
 u u 
 
 " 
 
 u 
 
 G. LcC. 
 
 113.0 
 
 .39 
 
 u u 
 
 half 
 
 u 
 
 W. C. S. 
 
 58.3 
 
 .41 
 
 u a 
 
 U 
 
 u 
 
 G. LeC. 
 
 58.3 
 
 .41 
 
 Scc( 111(1 " 
 
 wliolo 
 
 u 
 
 W. C. S. 
 
 (>(>.'> 
 
 .40 
 
 " '* 
 
 
 
 E. D. D. 
 
 ()+.(i 
 
 .39 
 
 
 .40 (3) 
 
 In view of the (lillicullies of the e\i)eiiiiu ut the consistency of the 
 detertninatinn is gratifying. 'I'lie average result of I he ■^i\ (iil.inii- 
 nalions is ])robai)ly correct williiu two per cent. 
 
 Il is to be nt)ted, lK)we\i'r, that this value, .Kt, is the ditfiieni-e 
 between the absorbing jjower of the person and the al)sorbing power 
 of t he settee and floor which, when tli<' audience left the room, look 
 ils i)lace as an absorbent. 1 1 is evident tiial the experiments de- 
 lerniincd I he difference between the two, while in subse(|uent cal-
 
 58 RKVKHin-:i{ATI()N 
 
 culalions we shall be concerned with the absohite absorl)ing power 
 of the audience. 'I'o (K-terniine this, on a following night all the 
 settees were carried out of the room, observations being taken be- 
 fore and after the change. From llu- dala lliiis obtained the absorb- 
 ing power of each settee accommodating five persons was found to 
 be .0;}!). or for a single seat .0077. Of necessity the floor still re- 
 mained, i)ut from a knowledge of its construction the absorbing 
 power of as much of the floor as is covered by one person was cal- 
 culated to be .0.30. Adding these together we get as the absorbing 
 power of an audience, seated with moderate compactness, .44 per 
 person. 
 
 In some subsequent work it will be necessary to know the ab- 
 sorbing power of an audience, not per person, but per square meter, 
 the audience being regarded broadly as one of the bounding sur- 
 faces of the room. As each person occupied on an average .40 of a 
 square meter of floor area, it is evident that the absorbing power 
 per square meter was .96 of a unit. 
 
 Under certain circumstances the audience will not be compactly 
 seated, but will be scattered about the room and more or less isolated, 
 for example, in a council-room, or in a private music-room, and it is 
 evident that under these conditions the individual will expose a 
 greater surface to the room and his absorbing power will be greater. 
 It is a matter of the greatest ease to distinguish between men and 
 women coming into a small room, or even between different men. 
 In fact, early in the investigation, two months" work — over three 
 thousand observations — had to be discarded because of failure to 
 record the kind of clothing worn by the observer. The coefficients 
 given in the following table are averages for three women and for 
 seven men, and were deduced from experiments in the constant- 
 temperature room. 
 
 Absorbing Power of an Audience 
 
 Audience per square meter 96 
 
 .\udience per person 44 
 
 Isolated woman 54 
 
 Isolated man 48 
 
 "When an audience fills the hall one is but little concerned with 
 the nature of the chairs — acoustically, but otherwise this becomes
 
 ABSORBING POWER OF AN AUDIENCE 59 
 
 a matter of considerable inij)ortanoe. The settees in the lecture- 
 room of the Physical Laboratory, already mentioned, are of plain 
 ash, and have solid seats, and vertical ribs in the back; they are 
 without upholstering; and it is interesting, in order to note the 
 agreement, to compare the absorbing power of such settees per single 
 seat, .0077, with that of the "bent wood" chairs in the Boston 
 Public Library, .0082, which are of similar character. In contrast 
 may be placed the chairs and settees in the faculty-room, which 
 have cushions of hair covered with leather on seat and back. In 
 the same table will be entered the absorbing power of Sanders 
 Theatre cushions, which are of hair covered with canvas and light 
 damask, and of elastic-felt cushions — cotton covered with corduroy. 
 
 Absorbing Power of Settees, Chairs, axd Ccshions 
 
 Plain ash settees 039 
 
 " " " per single seat 0077 
 
 " " chairs "bent wood" OOSi 
 
 Upholstered settees, hair and leather 1.10 
 
 " " per single seat 28 
 
 " {-hairs similar in style 30 
 
 Hair cusliions per seat 21 
 
 Elastic-felt cushions per seat 20 
 
 A case has arisen evin in the present paper where it is necessary 
 to know the absorbing power of paintings on canvas, and the ques- 
 tion may not infrequently arise as to how much service is secured 
 — or injury incurred — acoustically by their use in particular 
 rooms. The oil paintings in the faculty-room, 10 in number, with 
 a total area, 19.9 square meters, gave opportunity for the determi- 
 nation of the desired coefficient; but a question arises in regard to 
 the method of reckoning the area. Thus, different coefficients are 
 obtained according as one measures the canvas only, or includes 
 the frames. The latter method, on the whole, seems best, althougii 
 most of the absori)ti()n is probably by tlic canviis. 
 
 The coefficient for house plants, which may be of piissing. and 
 possibly practical, interest, was even harder to express. A green- 
 hou.se, 140 cul)ic iiulers in volunu-, and in whicii plants occupied 
 about one-quarter of the space, showed an al)sorbing jiower greater 
 lliaii that due to the walls and floor by 4 units, or .11 per cubic 
 meter of plants. It would l>e of greater value to dcterinine the
 
 eO HKVKRBKUATIOX 
 
 ahsorhinp power of such plants as arc used, often very extensively, 
 in (lecorafiiig on festival occasions, hut no opportunity lias yet 
 pres«-iit(il itself. 
 
 Ainonj; the cloths used in decorations, cheesecloth and cretonne 
 may l)e taken as types. The first is an American Rauze. 48 grams 
 to the s<|uare meter. The second is an ordinary cotton-jjrint cloth, 
 184 frrams |)er stjuare meter. Shelia. an extra quality of chenille, 
 is a regular curtain material used only in ])ermanent decorations. 
 
 Linolciiiii and cork are commercial products, the first used as 
 floor covering and the .second in walls, liotli were tested lying 
 l<K>seIy on the floor; cemented in place, their values would probably 
 he different. 
 
 The carijct rug is a heavy pile carpet about .8 centimeter thick. 
 
 In the following table the values are per square meter, except in 
 the case of plants, where the coefficient is per cubic meter: 
 
 Miscellaneous 
 
 Oil paintings, inclusive of frames 28 
 
 House planls 11 
 
 Carpet rugs 20 
 
 Oriental rugs, extra heavy 29 
 
 Ciieesecloth 019 
 
 Cretonne eloth 15 
 
 Slielia curtains 23 
 
 Hairfelt, '-'..5 em. tliiek. 8 cm. from wall 78 
 
 Cork, •i.o em. thick, loose on floor 16 
 
 Linoleimi, loose on floor 12 
 
 ( AL( ILATION IN ADVANCE OF CONSTRUCTIOX 
 
 In the present paper it is the purpose to show the application of 
 the preceding analysis and data, taking as an exani]jle the design 
 of the new Boston Music Hall' now under construction, Messrs. 
 McKini. Mt ad & White, architects. 
 
 In the introductory pai)er the general i)rol)lem of architectural 
 acoustics was shown to be a fairly comiilicated one, and to involve 
 in its solution considerations of loudness, of interference, of reso- 
 nance, and of reverberation. All these points received considera- 
 tion while the Hall was being designed, but it is proposed to discuss 
 
 ' Huston Sympliony Hall.
 
 CALCULATION IN CONSTRUCTION 61 
 
 here only the case of reverberation. In this respect a ninsic hall is 
 peculiarly interesting. In a theatre for dramatic performances, 
 where the music is of entirely subordinate importance, it is desirable 
 to reduce the reverberation to the lowest possible value in all ways 
 not inimical to loudness; but in a music hall, concert room, or 
 opera house, this is (Iccidcdiy not the case. To reduce the rever- 
 beration in a hall to a niiniiiuiiii. or lo make the conditions such that 
 it is very great, may, in (■cilain ca.ses, present [jractical difficulties 
 to the architect — the()reticall\- it presents none. To adjust, in 
 original design, the reverberation of a hall to a particular and ap- 
 proved value refiuires a study of conditions, of materials, and of 
 arrangement, for wliicli it has been tlie object of tlie preceding 
 l>ai)ers to prepare. 
 
 It is not at all difficult to show a priori that in a liall for orches- 
 tral nuisic the reverberation siiould neither be very great, nor, on 
 the oliitT hand, cxtremi'ly small. However, in this matti-r it was 
 not necessary to rely on theoretical considerations. Mr. Gericke, 
 the conductoi- of ilic Boston Syni|)ii()n\- Orchestra, made the state- 
 ment that an orclicstra, meaning b_\- this a symphony orchestra, is 
 never heard to tiie best advantage in a theatre, that the sound 
 seems o])pressed, and thai a ccrlaiii amount of rcNcrberation is 
 necessary. An examination of all the availal)le plans of the halls 
 cited as more or less satisfactory models, in the preliminary dis- 
 cussion of the plans for the new hall, showi'd that they were such 
 as to give greater re\('rberati()n than tiie ordinary theatre style of 
 construction. While several jjlans were thus cursorily i-xamined 
 the real discussion was based on only two buildings — the i)resen! 
 Boston Music Ilall and tlu- Leipzig (iewantlhaus; one was familiar 
 to all and inunediately accessible, the other familiar to a mmilur- of 
 those in consullal i<in, and iK |ilan> m grcal dcl.-nl were to lie 
 found ill Iht.'i ucuc (icu'duillidus m Lajriij. ran I'liiil linipiiis innl II . 
 Srlnnicdcn. It should, pcrliai)s, lie immedialely added that iicillier 
 hall served as a modi! arcliitecturall.w but that i)olh were u>ed 
 rather as defiiiilions and starting puiul-. dii llic a(()U-~l ical xide of 
 the di.scu.ssion. The old Music Ilall wa-- no! a desirable model in 
 e\'ery respect, even acoiislically. and tlic l,<ipzig (lewaiidliaiis. 
 having a sealing capacity al)out that of Sanders 'I'heatre, IJUO,
 
 (5^2 UKVKIUJKKATION 
 
 was so small lus to he debarred from serving directly, for this if for 
 no other reason. 
 
 The history of tlie new hall is about as follows: A number of 
 years ago. when the subject wiis first agitated, Mr. McKim prepared 
 plans and a model along classical lines of a most attractive audi- 
 toriuni. and afterwards, at Mr. Iligginson's instance, visited 
 Europe for the i)urpose of consulting with nnisical and scientific 
 authorities in France and Germany. But the Greek Theatre as a 
 music hall was an untried experiment, and l)ecause untried was re- 
 garded as of uncertain merits for the purjwse by the conductors 
 consulted by Mr. Iligginson and Mr. McKim. It was, therefore, 
 abandoned. Ten years later, when the project was again revived, 
 the conventional rectangular form was adopted, and the intention 
 of the building connnittee was to follow the general proportions and 
 arrangement of the Ix'ijjzig Gewandhaus, .so enlarged as to increase 
 its seating capacity about seventy per cent; thus making it a little 
 more than equal to the old hall. At this stage calculation was first 
 applied. 
 
 The often-repeated statement that a copy of an auditorium 
 does not necessarily possess the same acoustical qualities is not 
 justified, and invests the subject with an unwarranted mysticism. 
 The fact is that exact copies have rarely been made, and can hardly 
 be expected. The constant changes and improvements in the ma- 
 terials used for interior construction in the line of better fireproofing 
 — wire lath or the ai)i)lication of the plaster directly to tile walls — 
 have led to the taking of liberties in what were perhaps regarded as 
 nonessentials; this has resulted, as shown by the tables, in a 
 changed absorbing power of the walls. Our increasing demands 
 in regard to heat and ventilation, the restriction on the dimensions 
 enforced by location, the changes in size imposed by the demands 
 for seating capacity, have prevented, in different degrees, copies 
 from being cojjies, and models from successfully serving as models. 
 So different have been the results under what was thought to be 
 safe guidance — but a guidance imperfectly followed — that the 
 belief has become current that the whole subject is beyond control. 
 Had the new Music Hall been enlarged from the Leipzig Gewandhaus 
 to increase the seating capacity seventy per cent, which, proportions 
 being preserved, would have doubled the volume, and then built, as
 
 CALCn.ATION IN CONSTRUCTION GS 
 
 it is being built, according to the most modern methods of fireproof 
 construction, the result, unfortunately, would have been to con- 
 firm the belief. No mistake is more easy to make than that of 
 copying an auditorium — but in different materials or on a differ- 
 ent scale — in the expectation that the result will be the same. 
 Every departure must be compensated by some other — a change 
 in material by a change in the size or distribution of the audience, 
 or perhaps by a partly compensating change in the material used 
 in some other part of the hall — a change in size by a change in 
 the proportions or shape. For moderate departures from the 
 model such compensation can be made, and the model will serve 
 well as a guide to a first approximation. When the departure is 
 great the approved auditorium, unless discriminatingly used, is 
 liable to be a treacherous guide. In tin's case the departure was 
 necessarily great. 
 
 The comparison of halls should be based on the duration of the 
 residual sound after the cessation of a source that has produced 
 over the hall some standard average intensity of sound, — say one 
 million times the minimum audible intensity, 1,000,000 i'. The 
 means for this calculation was furnished in the fifth paper. The 
 values of T' and a for the three halls under comparison are shown 
 on the next page. 
 
 Tlu> length given for the Leipzig Gewandhaus, 88 meters, is 
 measured from the organ front to the architecturally principal wall 
 in the rear. On the floor and by boxes in the balconies the seats 
 extend 3 meters farther back, making the whole length of the hall, 
 exclusive of the organ niche, 41 meters. This increases the vohune 
 of the hall about '200 cubic meters, making the total volume 11,400 
 cubic meters. 
 
 'IIic lieight givi'U for the new Boston Music Hall, 17.!), is the 
 average heiglit from the sloping floor. The length is measured on 
 the floor of the main part of the hall; aboxc the second gallery it 
 extends back !-2.74 meters, giving an adilitional volume of 380 cubic 
 meters. The stjige, instead of being out in the room, is in a con- 
 tracted recess having a depth of 7.!) meters, a breadth, front and 
 back, of 18.8 ami 1.8.0. respectively, and a height, front and back, 
 of 13.4 and 10.0, resjiectively, with a volume of l,oOO cubic meters. 
 The height of the stage recess is determined by the absolute re-
 
 (il 
 
 RKNKRRKRATIOX 
 Dimensions of the Three Hali;s in Meters ' 
 
 I^nfrth . 
 Hmiilth 
 tlfight 
 
 Volume . 
 
 LeJDiiK Gcvaodhaiu Boston Music Hall. Boston Music Hall, 
 Old New 
 
 (luiroiiu'iits ol' (lif lar^H' orKaii lu be buill l)y Mr. George S. Hutch- 
 ings. This organ will extend across the whole breadth of the stage. 
 The lohil volume of thf new Roston Music Hall is, therefore, 
 1S..'50U cubic meters. 
 
 In the following table of materials in the three halls no distinction 
 is made between plaster on wire lath and plaster on wood lath, the 
 experiments recorded in tlie preceding paper having shown no cer- 
 tain difference in absorbing power. The areas of wall-surface are 
 exi)ressi'd in s(|uare meters. The number of persons in the audience 
 is reckoned from the number of seats, no account being taken of 
 standing room. 
 
 ' Dlmensions of the Thuke Halls ix Feet 
 
 Leipzig 
 Ge wand ha us 
 
 Boston 1 Boston 
 
 Music Hall. Old Music Hall. New 
 
 Letigth. 
 Breadth 
 Height . 
 
 Volume. 
 
 (130) 
 75 
 59 
 
 (575,000) 
 
 The length given for the I>eipzig Gcwandhaus, 144 feet, is measured from the organ front 
 to the arohite<-luralIy principal wall in the rear. On the floor and by boxes in the balconies 
 the seats extend 10 feet farther back, making the total length of the hall, exclusive of the 
 organ niche. 1S4 feet. This increases the volume 7,000 cubic feel, making the total volume 
 ■t(l7,(MH) cul)ic feet. 
 
 The height given for the new liiill, .")!) feel, is the average height from the sloping floor. 
 The length is measured on the HiMir of the main part of the hall; above the second gallery it 
 extends back !) feet, giving an adilitional volume of '20,000 cubic feet. The stage, instead of 
 being out in the room, is in a contracted recess, having a depth of "iii feet, a breadtii, front and 
 buck, of fit) feet and 45 feet, respectively, and a height, front and back, of 44 feet and 35 feet, 
 respectively, with a volume of 54,000 cubic feet. The total volume of the new Music Hall is, 
 therefore, r)4n,0(tn i ubic feet.
 
 CALCULATION IN CONSTRUCTION 
 
 65 
 
 Absorbing Material 
 
 Leipzig 
 Gewandhaus 
 
 Boston Music Hall, 
 Old 
 
 Boston Music Hall, 
 New 
 
 Piaster on lath . 
 I'histtT on tilo. . 
 
 (;lass 
 
 Wood 
 
 Drapery 
 
 Audience: 
 
 on floor 
 
 in Isl l>aleony 
 in 2d balcony 
 
 Total audience. 
 
 Orchestra 
 
 2,200 
 
 
 
 17 
 
 233 
 
 80 
 
 990 
 
 494 
 
 33 
 
 1,.-.17 
 
 80 
 
 3,030 
 
 
 
 55 
 
 771 
 
 4 
 
 1,251 
 C80 
 460 
 
 2,391 
 
 80 
 
 1,040 
 
 1,830 
 
 22 
 
 C25 
 
 
 
 1,400 
 (iOO 
 507 
 
 2,579 
 
 80 
 
 'I'lic (Inipcry in I In- Leipzig Gewandhaus will he rated as shelia, 
 and in I lie old Music Hall as cretonne, to which it approximates in 
 each case. It is an almost needless nfiiuincnl to rate differently 
 the orchestra and the audience merely because the members of the 
 orchestra sit more or less clear of each other, but for the sake of a 
 certain formal completeness it will be done. For the above materials 
 the coefficients, taken from the preceding paper, are as follows: 
 
 Coefficients of Absorption 
 
 Plaster on latii 033 
 
 Plaster on tile 025 
 
 Class 027 
 
 Wood 061 
 
 / shelia 23 
 
 Drapery < , ,- 
 
 [ cretonne »•> 
 
 Audience per person 44 
 
 Orchestra per man 48 
 
 In Ihe table (p. 07) is entered liie total absorbing power con- 
 tributed by each of these elements. As this is the first example of 
 such cilciil;!! loll ;ill ihc clcmciils will be slinwn. a!llioui;li it will 
 liiiii be iimiiediateiy evidnit that noimc are of wholly negligible 
 magnil udc.
 
 —.7 8 »l.- 
 
 FiG. 20. The Leipzig Gewandhaus. 
 
 .- Lmut 
 
 ijuyimji 
 
 n B III — t 
 
 H 
 
 a 
 
 Q. 
 
 ffl IfflllfflllB 
 
 M 
 
 301 
 
 ■:iu.-i ni.- 
 
 I-IG. il. The Old Boston Music Hall. 
 
 3».5 m- 
 
 FiG. ii. The New Boston Music Hall.
 
 CALCULATION IN CONSTRUCTION 
 
 67 
 
 Absorbing Power 
 
 
 Leipzig 
 Gewandhaus 
 
 Bostoa Music Hall, 
 Old 
 
 Boston Music Hall, 
 New 
 
 Plaster on 
 
 lath 
 
 73 
 
 II 
 
 0.4 
 
 14 
 
 18 
 
 667 
 
 38 
 
 100 
 
 
 1.5 
 47 
 0.6 
 1,052 
 38 
 
 34 
 
 Piaster on 
 
 tile 
 
 46 
 
 Glass 
 
 
 0.6 
 
 Wood 
 
 38 
 
 Drapery 
 
 
 
 Audience 
 
 1,135 
 
 Orchestra 
 
 38 
 
 
 
 
 Total = a 
 
 810 
 
 1,239 
 
 1,292 
 
 
 
 
 V and a being determined for each of the three halls, the dura- 
 tion, T, of the residual sound after standard initial intensity can be 
 calculated. 
 
 The results, in seconds, are as follows: 
 
 Leipzig Gewandhaus 'i.SO 
 
 Old Boston Music Hall ^.44 
 
 New Boston Music Hall '2.31 
 
 In other words, the new hall, although having a seating capacity 
 for over a thousand more than the Gewandhaus and nearly two 
 hundred more than the old hall, will have a reverberation between 
 the two, and nearer that of the Gewandhaus than that of the old 
 hall. 
 
 It is interesting to contra.st this with the result that would have 
 been obtained had the plan been followed of reproducing on an en- 
 larged scale the Gewandhaus. Assuming perfect reproduction of 
 all proportions with like materials, the volume would have been 
 25,300 cubic meters, and the absorbing power 1,370, resulting in the 
 value, T = 3.0'2. This woulil have differed from the chosen result 
 l)y an amount tiiat would have l)een very noticeable. 
 
 The new IJoston Music Hall is, therefore, not a copy of tiie 
 Gewandhaus, but tlie desired results have been attained in a very 
 different way. 
 
 A few general considerations, not directly c(mnected with rever- 
 beration, UKiy be of interest. The three halls are of nearly the same 
 length on the floor; but in the old hall and in the Gewandhaus the
 
 68 Hi:M;i{i{i;RAri()X 
 
 plat form for tin* orclu-stra is out in I lie liall. and tlu' f,'aIl(Tie.s extend 
 alon^r l)olli sides of it; wliile in the new hull Ihe orchestra is not out 
 in tile main hody of tlie room, and for this roivson is slightly farther 
 from the rear of the hall; l)ut this is more than compensated for in 
 respec'l to loudness by the orchestra being in a somewhat contracted 
 stage recess, from the side walls of which the reflection is better 
 l)eeause they are nearer and not occupied by an audience. Also it 
 may be noted that the new hall is not so high as the old and is not 
 so broad. 
 
 Thus is opened up the ([uestion of loudness, and this has been 
 solved to a first ajiproximation for the case of sustained tones. 
 But as the series of papers now conchided is devoted to the question 
 of reverberation, this new problem must be reserved for a subse- 
 quent discussion.
 
 ARCHITFXTURAL ACOUSTICS^ 
 
 INTRODUCTION 
 
 1 HE prohk'in of iircliiti'ctiiral ucoiislics ri'ciuiivs for its complete 
 solution two distinct lines of invest ij^at ion, one to determine (|iian- 
 titatively the physical conditions on which loudness, reverberation, 
 resonance, and the allied phenomena depend. I lie oilier to deleriiiine 
 the intensity which each of these should have, what conditions are 
 best for the distinct audition of sjjeech. and what effects are best for 
 music in its various forms. One is a purely ])hysical investigation, 
 and ils conclusions should be based an<l ^lll>uld be disputed only on 
 scientific grounds; the other is a matter of judf^iiient and taste, and 
 its conclusions are weif.rhly in ])ro|)orl ion to the weight and unaiiinutj' 
 of the iiuthorily in which they find their source. For this re;uson, 
 these pajHTs are in two series, 'ihe articles which appeared six 
 years ago began the first, and the |)a])er immediately following is 
 the begimu'ng of the second. 
 
 Of the first .series of papers, which have to do with the ])urely 
 physical side of the problem, only one pajjcr has as yet been i)ub- 
 lislicd. 'I'his conlaiiied a di.scussion of reverberation, eomplele as 
 far as one note is concerned. There is on hand considerable material 
 for a paper I'xiending this discussion to cover the whole range of the 
 musical scale, and therefore furiii>liing a basis for the discussion of 
 whiit has sometimes been called the musical (|iiality of an audito- 
 rium, 'i'lii'i'e li.i- also l>eeu eolieeled a eerlaiu amount of data ill 
 regard to loudni-ss. resonance, interference, eclux's, irregularitit's of 
 air curri'nts and lemperalure, and the transmission of sound through 
 walls and partiti(jns, — all of which will ajipear as soon as a com- 
 plete ]n-esentation is j)ossil)le in each ( a>e. i'l.ieh pri(l)lem iia^ lieen 
 taken up as it has been brought to the writer's attention by an 
 architect in coiisullal ion either o\-er |)lans or in regard to a coin- 
 ph'ted buihling. lliis method is slow, but it has Ihe advantage of 
 
 ' l'r<)Of<iling.s (if tile .Viiicriran .\(iulomy nf .\rls iiiul .Scit-iK-cs, vol. xlii, no. i, .Iiiiio, lOIIO. 
 
 (Ill
 
 70 AH( IIITECn'RAL ACOUSTICS 
 
 riiakiiig (Ik- work i)r;iclic;il. and may Ix- rt-lii'd on lo i)rev(.'iil the 
 inafinificalion to undue importance of scientifically interesting but 
 practically subordinate points. On the other hand, there is the 
 danger liiat it may lead to a fragmentary jjresciilation. An effort 
 has been made to guard against this, and the effort for completeness 
 is the reason for delay in the appearance of some of the papers. 
 Sufficient jjrogress has been made, however, to justify the assertion 
 llial the physical side of the problem is solvable, and that it should 
 be possible ultimately to calculate in advance of construction all 
 the acoustical (|ualilies of an auditorium. 
 
 'riiu> far it is a legitimate problem in physics, and as such a 
 reasonable one for the writer to undertake. 
 
 The second part of the problem, now being started, the question 
 as to what constitutes good and what constitutes poor acoustics, 
 what effects are desirable in an auditorium designed for speaking, 
 and even more especially in one designed for music, is not a question 
 in physics. It is therefore not one for which the writer is especially 
 qualified, and would not be undertaken here were it not in the first 
 place absolutely necessary in order to give effect to the rest of the 
 work, and in the second place were it not the plan rather to gather 
 and give expression to the judgment of others acknowledged as 
 (|ualified to speak, than to give expression to the taste and judg- 
 ment of one. It is thus the purpose to seek expert judgment in 
 regard to acoustical effects, and if possible to present the results in 
 a form available to architects. This will be slow and difficult work, 
 and it is not at all certain that it will be possible to arrive, even ulti- 
 mately, at a finished product. It is worth undertaking, however, if 
 the job as a whole is worth undertaking, for without it the physical 
 side of the investigation will lose much of its practical value. Thus 
 it is of little value to be able to calculate in advance of construction 
 and express in numerical measure the acoustical quality which any 
 planned auditorium will have, unless one knows also in numerical 
 measure the acoustical quality which is desired. On the other hand, 
 if the owner and the architect can agree on the desired result, and 
 if this is within the limits of possibility considering all the demands 
 on the auditorium, of utility, architecture, and engineering, this 
 result can be secured with certainty, — at least there need be no
 
 ACCrRACY OF MUSICAL TASTE 71 
 
 uncertainty as to wlu-tlu'r it will or will not be attained in the com- 
 pleted building. 
 
 The papers following this introduction will be: The Accuracy of 
 
 Musical Taaie in regard to A rr/iifertiiral Acoustics, and Variation in 
 Reverberation with J'ariation in Pitch. 
 
 riri-; accuracy of musical taste ix regard 
 TO architectural acoustics 
 
 PIANO MUSIC 
 
 1 HE experiments described in this paper were undertaken in order 
 to determine the reverberation best suited to piano music in a music 
 room of moderate size, but were so conducted as to give a measure of 
 the acc-uracy of cultixaLcd lunsical iasle. Tlie lattiT jjoint is ()l)vi- 
 ously fundamental to the whole investigation, for unless musical 
 taste is precise, the ])r()b!em. at least as far as it concerns the design 
 of the auditorium for nuisical purposes, is indeterminate. 
 
 The first ()l)S('r\atii)ns in regard to the precision of nuisical taste 
 were obtained during tlic plaiming of the Boston Sjmiphony Hall, 
 Messrs. McKim, Mead, and White, Architects. Mr. Higginson, 
 Mr. Gericke. the conduc-tor of tlie orchestra, and others connected 
 with the Building Conunittee expre.s.sed opinions in regard to a 
 number of auditoriums. These buildings included the old Boston 
 Music Hall, at that time the home of the orchestra, and the places 
 visited l)v the orchestra in its winter trips, Sanders Theatre in 
 Cambridge, Carnegie Hall in New York, the Academy of Music in 
 Philadelphia, and the Music Hall in Baltimore, and in addition to 
 these the Leipzig Gewandliaus. By invitation of Mr. Higginson, 
 the writer accompanied the orchestra on one of its tri])s, made 
 measurements of all the hails, and calculated their reverberation. 
 The dimensions ami I lie in.ilcri.d of I lie Gewandhaus had been 
 
 publislied, and IV Ihesedala its re\-ci-l)craliiin also was cah-ulated. 
 
 The results of lhe.se mciusm-ements and calculations showeil that the 
 opinions expressed in regard to the several halls were entirely con- 
 sistent with the physical facts. That is to say, the reverberation in 
 those halls in wiiidi il was declared too gn-at was in point of physi- 
 cal meiisuremenl greater than in halls in which it was i)ronouncetl
 
 7^2 Ai{( iirrK(Tn{Ai> acoistks 
 
 loo small. This coiisisU-iicy gavf i-ncoiirafrciiUMit in tlic liope tliat 
 fill' pliysical proMi-iu was rral, ami tin- ciul to lu' allaiiied definite. 
 
 Mucli more <-lal)(>rate data on the accuraey of musical taste were 
 ol)tainfii four yt'ar> lalcr. l!t(»-', in coniiccl ion with the new l)uililiii<,' 
 of the New England Conservatory of Miisie, Messrs. Wheelwright 
 and Haven. Architects. The new building consists of a large audi- 
 torium surrounded on three sides hy smaller rooms, which on the 
 .second and lliird floors are used for purposes of instruction. These 
 smaller rooms, wlicn first occupied, and used in an unfurnished or 
 j)artially furnished condition, were found unsuital)le acoustically, 
 and the writer wius consulted by Mr. Haven in regard to their final 
 adjustment. In order to learn the acoustical condition which would 
 accural cly nucl the requirements of those who were to use the 
 rooms, an experiment was undertaken in which a number of rooms, 
 chosen as tyi)ical. were varied rapidly in resjject to reverberation by 
 means of temporarily introduced absorbing material. Approval or 
 disai)])roval of I lie acoustical quality of each room at each stage was 
 expressed by a connnittee chosen by the Director of the Conserva- 
 tory. At the close of these tests, the reverberation in the rooms was 
 mciisured by the writer in an entirely indci)cndcut nuinner as 
 described in the paper on Reverberation (1900). The judges were 
 Mr. (leorge W. Chadwick, Director of the Conservatory, and Signor 
 Orcsti Binibom', Mr. William H. Dunham, Mr. George W. Proctor, 
 anil Mr. William L. Whitney, of the Faculty. The writer suggested 
 and arranged the experiment and subsequently reduced the results 
 !o muncrical measure, but expressed no opinion in regard to the 
 quality of the rooms. 
 
 The merits of each room in its varied conditions were judged 
 solely by listening to piano music by ]Mr. Proctor. The character 
 of the nui>i(al compositions on which the judgment was based is a 
 matter of interest in this connection, but this fact was not appre- 
 ciated at, the time and no record of the selections was made. It is 
 only |)ossible to say that several short fragments, varied in nature, 
 were tried in eacli room. 
 
 As will be evident from the descriptions given below, the rooms 
 were so differently furnished that no inference as to the reverbera- 
 tion could be drawn from appearances, and it is certain tliat the
 
 ACClTiACY OF :\IT;SirAL TASTE 73 
 
 opinions were htused .solely on I lie qii;ilil\' ol' Uie room as heard in 
 the i)iiino music. 
 
 The five rooms chosen as typical were on the second floor of I lie 
 buildinf:^. The rooms were four meters high. Their volumes varied 
 from 74 to '210 cubic meters. The walls and ceilinjjs were finished in 
 plaster on wire lath, and were neither papered nor painted. There 
 was a piano in each room; in room .5 there were two. Tiie amount 
 of other iiirniture in tlie rooms varied <,n'eatly: 
 
 In room 1 there was a hare floor, and no furniture excej)t the 
 piano and piano stool. 
 
 Room '■2 had rugs on the floor, chairs, a sofa with pillows, table, 
 music racks, and a lanij). 
 
 Room :> had a carpet, chairs, bookcases, and a large number of 
 books, which, overflowint; I lie bookcases, were stacked along the 
 walls. 
 
 Room 4 had no carpet, but there were chairs and a small table. 
 
 Room 5 had a carpet, chairs, and shelia curtains. 
 
 Thus the rooms varied from an almost unfurnished to a reasonaI)ly 
 furnished condition. In all eases the reverberation was too great. 
 
 The experiment was begun in room 1. Tliere were, at the time, 
 besides the writer, five gentlemen in the room, the absorbing effect 
 of whose clothing, though small, nevertheless should be taken into 
 account in an accurate calculation of the reverberation. Thirteen 
 cushions from the seats in Sand<'rs Theatre, whose absorl)ing power 
 for sound liad been deterinined in an earliei' investigation, were 
 brought into the room. I'nder tliese conditioTi> the imanimous 
 opinion was that the room, as tested by the piano, was lifeless. 'I'wo 
 cushions were then removed from the room with a perceptible change 
 for the beltei- in the piano nuisic. 'i'hree more cushions were re- 
 moved, and tlieetfect was iimkIi lutler. 'l\vo more were then taken 
 out, leaving six cushions in I lie room, and I lie re>iilt met unanimous 
 approval. It was suggested liiat two more be removetl. This l)eing 
 done the re\-erberal ion was found to be loo great. The agreement 
 was then reached tlial the conditions produced by tlu- presi-nce ol 
 si.\ cushions were the most nearly satisfactory. 
 
 The e\|)erinu'nt was tiu'U contimied in Mr. Dunham's ro(»m, 
 numl)er ^i. Six gentlemen were present. Seven cushions were
 
 74 AHCmrKCTrUAL ACOUSTICS 
 
 hroiijjlit into tlio room. 'I'lif music showed an insiifficiont rever- 
 iHTiilion. Two of the cusliions wt-ro tlien taken out. The change 
 was reganled as a distinct improvement, and the room was satis- 
 factory. 
 
 Tn yir. Wliitney's room, number 3, twelve cushions, with which 
 it w;us th(>uf,'ht to overload the room, were found insufficient even 
 with the presence in this case of seven gentlemen. Three more 
 cushions were brought in and the result declared satisfactory. 
 
 In llif fourth room, five, eight, and ten cushions were tried be- 
 fore the conditions were regarded as satisfactory. 
 
 In Mr. Proctor's room, number 5, it was evident that the ten 
 cushions which had been brought into the room had overloaded it. 
 Two were removed, and afterwards three more, leaving only five, 
 before a satisfactory condition was reached. 
 
 This completed the direct experiment with the piano. 
 The i)ringing into a room of any absorbing material, such as these 
 cushions, affects its acoustical properties in several respects, but 
 principally in respect to its reverberation. The prolongation of 
 sound in a room after the cessation of its source may be regarded 
 either ;ls a case of stored energy which is gradually suffering loss by 
 transmission through and absorption by the walls and contained 
 material, or it may be regarded as a process of rapid reflection from 
 wall to wall with loss at each reflection. In either case it is called 
 reverberation. It is sometimes called, mistakenly as has been ex- 
 jilained, resonance. The reverberation may be expressed by the 
 duration of audibility of the residual sound after tjie cessation of a 
 source so adjusted as to produce an average of sound of some stand- 
 ard intensity over the whole room. The direct determination of 
 this, under the varied conditions of this experiment, was impracti- 
 cable, but, by measuring the duration of audibility of the residual 
 sound after the cessation of a measured organ pijx' in each room 
 without any cushions, and knowing the coefficient of absorption of 
 the cushions, it was jiossible to calculate accurately the reverbera- 
 tion at each stage in the test. It was impossible to make these 
 measurements inunediately after the above experiments, because, 
 although the day wjis an especially quiet one, the noises from the 
 street and railway traffic were seriously disturbing. Late the follow-
 
 ACCURACY OF MUSICAL TASTE 
 
 to 
 
 iiig night the conditions were more favorable, and a series of fairly 
 good observations was obtained in each room. ITie cushions had 
 been removed, so that the measurements were made on the rooms in 
 their original condition, furnished as above described. The appara- 
 tus and method employed are described in full in a series of articles 
 in the Engineering Record ' and American Architect for 1900. 
 The results are given in the accompanying table. 
 
 J 
 i 
 
 z 
 
 I 
 
 <£ 
 
 Gentlemen Present 
 
 9 
 
 u = 
 
 .e:s 
 
 ■£c 
 
 NiiiiilxT of Meters 
 of Cushions 
 
 Absorbing Power 
 of Cushions 
 
 Total Absorbing 
 Power 
 
 Reverberation in 
 Seconds 
 
 Remarks 
 
 1 
 
 74 
 
 5.0 
 
 
 
 
 
 
 
 
 
 5.0 
 
 2.43 
 
 Reverberation too great. 
 
 
 
 U 
 
 5 
 
 2.4 
 
 (1 
 
 
 
 7.4 
 
 1.64 
 
 Reverberation too great. 
 
 
 
 a 
 
 u 
 
 u 
 
 13 
 
 12.8 
 
 20.2 
 
 .60 
 
 Reverberation too little. 
 
 
 
 a 
 
 u 
 
 U 
 
 11 
 
 10.1 
 
 17.5 
 
 .70 
 
 Better. 
 
 
 
 M 
 
 a 
 
 u 
 
 8 
 
 7.3 
 
 14.7 
 
 .83 
 
 Better. 
 
 
 
 U 
 
 u 
 
 u 
 
 (i 
 
 5.5 
 
 12.9 
 
 .95 
 
 Condition approved. 
 
 
 
 a 
 
 u 
 
 u 
 
 4 
 
 3.(i 
 
 11.0 
 
 1.22 
 
 Reverberation too great. 
 
 i 
 
 91 
 
 6.3 
 
 
 
 
 
 
 
 
 
 (I.;! 
 
 2.39 
 
 Reverberation too great. 
 
 
 
 u 
 
 6 
 
 2.9 
 
 
 
 (1 
 
 9.2 
 
 1.95 
 
 Reverberation too great. 
 
 
 
 a 
 
 U 
 
 '• 
 
 7 
 
 (i.4 
 
 15.(i 
 
 .95 
 
 Reverberation too little. 
 
 
 
 u 
 
 u 
 
 u 
 
 .5 
 
 4.G 
 
 l;!.8 
 
 1.10 
 
 Condition approved. 
 
 S 
 
 210 
 
 14.0 
 
 
 
 
 
 
 
 
 
 14.0 
 
 2.40 
 
 Reverberation too great. 
 
 
 
 U 
 
 7 
 
 3.4 
 
 
 
 
 
 17.4 
 
 2.00 
 
 Reverberation too great. 
 
 
 
 u 
 
 tt 
 
 tt 
 
 12 
 
 11.0 
 
 28.4 
 
 1.21 
 
 Better. 
 
 
 
 a 
 
 tt 
 
 u 
 
 15 
 
 13.7 
 
 31.1 
 
 1.10 
 
 Condition approved. 
 
 4 
 
 133 
 
 8.8 
 
 
 
 
 
 
 
 
 
 8.3 
 
 2.65 
 
 Reverberation too great. 
 
 
 
 U 
 
 7 
 
 3.4 
 
 
 
 
 
 11.7 
 
 1.87 
 
 Reverberation too great. 
 
 
 
 u 
 
 a 
 
 u 
 
 6 
 
 5.5 
 
 17.2 
 
 1.2(i 
 
 Better. 
 
 
 
 u 
 
 u 
 
 u 
 
 10 
 
 9.1 
 
 20.8 
 
 1.09 
 
 Condition approved. 
 
 5 
 
 96 
 
 7.0 
 
 
 
 (1 
 
 (1 
 
 
 
 7.0 
 
 2.24 
 
 Reverberation too great. 
 
 
 
 ' « 
 
 4 
 
 l.i) 
 
 
 
 
 
 8.9 
 
 1.76 
 
 Reverberation too great. 
 
 
 
 tt 
 
 u 
 
 U 
 
 10 
 
 9.1 
 
 18.0 
 
 .87 
 
 Reverberation too little. 
 
 
 
 u 
 
 u 
 
 u 
 
 8 
 
 7.3 
 
 16.2 
 
 .98 
 
 Belter. 
 
 
 
 u 
 
 u 
 
 u 
 
 5 
 
 4.6 
 
 13.5 
 
 1.16 
 
 Condition approved. 
 
 < The iirticle in tlie Engineering Record is identical willi llio paper in llie .Xmoritun 
 Architect for 1900, reprinted in thi.s volume a» I'arl 1.
 
 76 Al{( IHTKCnUAI. ACOUSTICS 
 
 The lahlo is a n-coril of tin- first of \vli;it. it is liopcd, will he a 
 series of siieli exi)eriinents extending' to rooms of iiukIi larger dinien- 
 sioiis and to oilier kinds of inusie. It may well he, in fact it is 
 hiphly ])rohahle. tliat very much larger rooms would necessitate a 
 dilfcnnl amount of reverheration, lus also may other types of musical 
 instruments or the voice. As an example of such investigations, as 
 well as evidence of their need, it is here given in full. The foHowing 
 additional explanations may be made. The variation in volume of 
 the rooms is only threefold, corresponding only to such music rooms 
 as may he found in private houses. Over this range a j)erceptihle 
 variation in the retpiired reverheration should not he expected. The 
 third colunm in the table inchules in the absorbing power of the 
 room (ceiling, walls, furniture, etc.) the absorbing powers of the' 
 clothes of the writer, who was present not merely at all tests, but in 
 the measurement of the reverberation the following night. From 
 the next two columns, therefore, the writer and the effects of his 
 clothing are omitted. The remarks in the last column are reduced 
 to the form "reverberation too great," "too little," or "ajiproved." 
 The remarks at the time were not in this form, however. The room 
 was ])ronoimced "too resonant," "too much echo," "harsh," or 
 "dull," "lifeless," "overloaded," expressions to which the forms 
 adopted are equivalent. 
 
 If from the larger table the reverberation in each room, in its 
 most approved condition, is separately tabulated, the following is 
 obtained : 
 
 Roonu Reverberation 
 
 1 95 
 
 2 1.10 ^ 
 
 3 1.10 
 
 4 l.Oi) 
 
 5 1.16 
 
 1.08 mean 
 
 The final result obtained, that the reverberation in a music room 
 in order to secure the best effect with a piano should be 1.08, or in 
 round numbers 1.1, is in itself of considerable practical value; but 
 the five determinations, by their mutual agreement, give a numeri- 
 cal meiusure to the accuracy of musical taste which is of great 
 interest. Thus the maximum departure from the mean is .13 seconds,
 
 ACCURACY OF MTTSICAL TASTE 77 
 
 and the avi-ragc (IciKirlure is .05 seconds. Five is ratlier a snudl 
 number of observations on which to apply the theory of probaliilities, 
 bill, assuming that it justifies such reasoning, the probable error is 
 .O"^ seconds, — surprisingly small. 
 
 A clo.se in.spection of the large lal)le will bring out an interesting 
 fact. The room in which the approved condition differed most from 
 the mean was the first. In this room, and in this room only, was il 
 suggested by the gentlemen present that the experiment should be 
 carried further. This was done by removing two more cushions. 
 The reverberation was then l.'-H seconds, and this was decided to 
 be too much. 'I'he ])oiut to be observed is that l.'2^2 is further above 
 tlic nuiiii, l.OS, tliaii .95 is below. Moreover, if one looks over the 
 list in each room it will be seen that in every case the reverberation 
 corresponding to the chosen condition came nearer to the mean than 
 that of any other condition tried. 
 
 It is conceivable tlial had the rooms been alike in all respects and 
 required the same amount of cushions to accomplish the same re- 
 sults, the experiment in one room might have j)rejudiced the ex- 
 periment in tlu' next. But tlie rooms being diiVerent in size and 
 furnished so differently, an impression formed in one room as to the 
 iininlicr of cushions necessary could only be misleading if depended 
 on in the next. Thus the several rooms re(|uired (>, 5, 15, 10, and 5 
 cushions. It is further to be ob.served that in three of the rooms the 
 final condition was reached in working from an overloaded con- 
 dition, and in llic oilier two rooms from the opposite condition, — 
 in the one case by taking cushions out. and in the other by bringing 
 them in. 
 
 Before bcgiiiiiiiig I lie exi)eriiiieiit no explaiial ion was made of its 
 nature, and no di.scussion was held as to the adxantages and disad- 
 vantages of re\('il)(ialion. '{"lie gentlemen present were asked to 
 express their a|)])roval or disapproval of the room at each stagt' of 
 the experiment, and the iiiial ilecision seemed to be reached with 
 perfectly free unanimil.w 
 
 This surprising accuracy of nuisical taste is perhaps the explana- 
 tion of the rarity with which it is entirely satisfied, particularly 
 when the arciiilectiiral designs are left to chance in this res])ecl.
 
 78 Al{< IHTi;( irHAL ACOUSTICS 
 
 \AIUATI()N IN REVKRBERATIOX WITH 
 \ AIUAI'IOX IX PITCH 
 
 Six yoars ago thero wjus published in the Engineering Record and 
 the American Architect a series of papers on architectural acoustics 
 intended as a heginning in the general subject. The particular phase 
 of the subject under consideration was reverberation, — the continua- 
 tion of sound in a room after the source has ceased. It was there 
 shown to depend on two things, — the volume of the room, and the 
 absorbing character of the walls and of the material with which the 
 room is filled. It was also mentioned that the reverberation depends 
 in special cases on the shape of the room, but these special cases were 
 not considered. Tlie present paper also will not take up these special 
 cases, but postpone their consideration, although a good deal of 
 material along this line has now been collected. It is the object 
 here to continue the earlier work rather narrowly along the original 
 lines. The subject was then investigated solely with reference to 
 sounds of one pitch, C4 512 vibrations per second. It is the inten- 
 tion here to extend this over nearly tlic wliole range of the musical 
 scale, from Ci G4 to ('7 4096. 
 
 It can be shown readily that the various materials of which the 
 walls of a room are Constructed and the materials with which it is 
 filled do not have the same absorbing power for all sounds regard- 
 less of ])itch. Under such circumstances the previously published 
 work with ("1 .51'-2 must be regarded as an illustration, as a part of a 
 much larger problem, — the most interesting part, it is true, be- 
 cause near the middle of the scale, but after all only a part. Thus a 
 room may have great re\erberation for soimds of low pitch and very 
 little for sounds of high i)itch, or exactly the reverse; or a room may 
 have comparatively great reverberation for sounds both of liigh and 
 of low pitch and very little for sounds near the middle of the scale. 
 In other words, it is not putting it too strongly to say that a room 
 may have very different quality in different registers, as different 
 as does a musical instrument; or, if the room is to be used for 
 speaking purposes, it may have different degrees of excellence or 
 defect for a whisper and for the full rounded tones of the voice, 
 different for a woman's voice and for a man's — facts more or less
 
 VARIATION IN REVERBERATION 79 
 
 well recognized. Not to leave this as a vague generalization the 
 following cases may be cited. Recently, in discussing the acoustics 
 of the proposed cathedral of southern California in Los Angeles 
 with Mr. Maginnis, its architect, and the writer, Bishop Conaty 
 touched on this jjoint very clearly. After discussing the general 
 subject with more than the usual insight and experience, possibly 
 in part because Catholic churches and cathedrals have great rever- 
 beration, he added that he found it difficult to avoid pitching his 
 voice to that note which the auditorium most prolongs notwith- 
 standing the fact that he found tliis the worst pitch on which to 
 speak. This brings out, perhaps more impressively because from 
 practical experience instead of from IIicoi('ti(:;il considerations, the 
 two truths that auditoriums have very ditfcrent reverberation for 
 different pitches, and that excessive reverberation is a great hin- 
 drance to clearness of enunciation. Another incident may also serve, 
 that of a church near Boston, in regard to which the writer has just 
 been consulted. The present pastor, in describing the nature of its 
 acoustical defects, stated that diff<M-ent speakers had different de- 
 grees of difficulty in making themselves heard; that he had no diffi- 
 culty, liaving a rut her liigh pitched voice; but that the candidate 
 before him, with a louder l)ut mucli lower voice, failed of the ap- 
 j)ointment because unable to make himself heard. Practical ex- 
 perience of the difference in reverberation with variation of pitch 
 is not unusual, but the above cases are rather striking examples. 
 Corresponding effects are not infrequently observed in halls devoted 
 to music. Its observation here, however, is marked in the rather 
 complicated general effect. Tlu- full discussion of this belongs to 
 another series of papers, in which will be taken up the subject of the 
 acoustical effects or conditions that are desirable for nuisic and for 
 speech. AVhile this pha.se of the subject will not be discussed here 
 at length, a little consideraticm of the data to be presented will show 
 how j)roiu)unct'd thesi- effects may l)e and how important in the 
 general subject of architectural acoustics. 
 
 In order to show the full significance of this extension of the in- 
 vestigation in regard to reverberation, it is necessary to point out 
 some features whieli in earlier i)apers wen- not especially empha- 
 sized. Primarily the investigation is concerned with the subject of
 
 80 AK( IHTi:( Tri{Ai, ACOrSTICS 
 
 rfVi-rluTiitioii. lliat is lo say, with tlu- suhji-cl of tli(> continuation of 
 a soiintl ill a nioin after tlu- sourco lia.s coasi'd. The iinnudiale etl'oct 
 of revfrluTatioM is that each nolo, if it he music, each syllable or 
 l>art of a syllal)lf. if it l)e speech. coMliiiucs its soiiml for sonic lime. 
 and i»y its prolonf,'at ion overlaps the succeediuii' notes or syllables, 
 Itarnionionsly or inliarnioniously in nnisic, and in speech always 
 towards confusion. In the case of .sjH'cch it i.s inconceivable that 
 this prolongation of I lie sound, this reverberation, should have any 
 other effect than that of confusion and injury to the clearness of the 
 enunciation. In music, on the other hand, reverberation, unless in 
 excess, has a distinct and i)ositi\(' advantage. 
 
 Perhaps this will be made more clear, or at least more easily 
 realized and :ipi)re(iatcd, if we take a concrete example. Given a 
 room comparatively empty, with hard wall-surfaces, for example 
 plaster or tile, and having in it comparatively little furniture, the 
 amoimt of reverberation for the sounds of about the middle register 
 of the double-bass viol and for the sounds of the middle register of 
 the violin will be very nearly though not exactly ecjual. If, how- 
 ever, we bring into the room a quantity of elastic felt cushions, 
 sufficient, let us say. to acconunodate a normal audience, the effect 
 of these cushions, the audience being supposed absent, will be to 
 diminish very much the reverberation both for the double-bass viol 
 and for tlu- violin, but will diminish them in very unc(|ual amounts. 
 The reverberation will now be twice as great for the double-bass as 
 for the violin. If an audience comes into the room, filling up the 
 seats, the reverberation will be reduced still rurlhcr anil in a still 
 greater disproportion, so that with an audience entirely filling the 
 room the reverberation for the violin will be less than one-third that 
 for the double-bass. When one considers that a difference of five 
 per cent in reverberation is a matter for approval or disapproval on 
 the part of musicians of critical taste, the importance of considering 
 these facts is obvious. 
 
 This investigation, nominally in regard to reverberation, is in 
 realit\ laying the foundation for other phases of the problem. It 
 has as one of its necessary and immediate results a determination of 
 the coefficient of absori)tion of sound of various materials. These 
 coefficients of absorjjtion, when once known, enable one not merely
 
 VARIATION IN REVERBERATION 81 
 
 to Ciilculalc llu' i)rolongation of tlu' sound, hul also to calculate the 
 average loudness of sustained tones. Thus it was shown in one of 
 the earlier papers, tliough at that time no very great stress was laid 
 on it, that the average loudness of a sound in a room is proportional 
 inversely to the absorbing powi-r of the material in the room. There- 
 fore the data which are being presented, covering the whole range 
 of the musical scale, enable one to calculate the loudness of different 
 notes over that range, and make it possible to show what effect the 
 room has on the piano or the orchestra in different parts of the 
 register. 
 
 'I'o illustrate this by the example above cited, if the double-bass 
 and the violin produce the same loudness in the open air, in the bare 
 room with hard walls both would l)e reenforced about ec|ually. The 
 elastic felt brougiit into the room would tieeidedly diminish this re- 
 enforcement for both instruments. It would, however, exert a much 
 more pronounced effect in the way of diminishing the reenforcement 
 for the violin than for the double-bass. In fact, the balance will be 
 so affected that it will rec|uire two violins to produce the same vol- 
 ume of sound as does one double-bass. The audience coming into 
 the room will make it necessary to use three violins to a double- 
 bass to secure the same balance as before. 
 
 Both cases cited above are only broadly illustrative. As a matter 
 of fact the effect of the room and the effect of the audience in the 
 room is perceptibly different at the two ends of the register of the 
 violin and of the double-bass viol. 
 
 'i'liere is still a third effect, which must be considered to appre- 
 ciate fully the i)ractical significance of the results that are being 
 presented. This is the effect on the quality of a sustained tone. 
 Every musical tone is composed of a great number of i)arlial tones, 
 the predominating one being taken as tlic fundamental, and its 
 pitch as the ])iteh of the sound. The otlier partial tt)nes are re- 
 garded as giving (|ualily or color to the fundamental. The musical 
 quality of a tone depends on the relatixc intensities of the overtones. 
 It has been customary, at least nn the |)arl of pliysicists, to regard 
 tin- relative intensities of the overtones, which define the ((ualil\' of 
 the soun<l, as de|)eniling sim|)ly on the sourer from which the sound 
 originates. Of course, jjrimarily, this is true. Nevertheless, while
 
 8« ARC IHTECTURAL ACOUSTICS 
 
 llu- source drfitu-s tlic relative intensities of the issuing sounds, their 
 actual intensities in the room depend not merely on that, but also, 
 and to a surprising degree, on the room itself. Thus, for example, 
 given an eight-foot organ pipe, if blown in an empty room, such as 
 that described above, the overtones would be j)ronounced. If ex- 
 actly the same i)ipe be blown with the same wind pressure in a room 
 in which the seats have been covered with the elastic felt, the first 
 iiplKT p;irlial will bear to the fundamental a ratio of intensity 
 dimiin'shed over 40 per cent, the second upper partial a ratio to the 
 fundamental diminished in the same per cent, the third upper 
 l)artial a ratio dimiuisiied over 50 per cent, while the fourth upper 
 partial will bear a ratio of intensity to the fundamental diminished 
 about 60 per cent. Quality expressed numericallj' in this way 
 probably does not convey a very vivid impression as to its real 
 effect. It may signify more to say merely that the change in quality 
 is very pronounced and noticeable, even to comparatively imtrained 
 ears. On the other hand, if one were to try the experiment with a 
 six-inch instead of with an eight-foot organ pipe, the effect of 
 bringing the elastic felt cushions into the room would be to increase 
 the relative intensities of the overtones, and thus to diminish the 
 purity of the tone. 
 
 All tones below that of a six-inch organ pipe will be purified by 
 bringing into the room elastic felt. All tones above and including 
 tiiat i)itch will be rendered less pure. The effect of an audience 
 coming into a room is still different. Assuming that the audience 
 hii-s filled the room and so covered all the elastic felt cushions, the 
 effect of the audience is to purify all tones up to violin C4 512, and 
 to \ia\c very little effect on all tones from that pitch upward. On 
 very low tones the effect of the audience in the room is more pro- 
 nounced. For example, again take Ci 64, the effect of the audience 
 will be to diminish its first overtone about 60 per cent relative to 
 the fimdamental and its second overtone over 75 per cent. 
 
 The effect of the material used in the construction of a room, and 
 the contained furniture, in altering the relative intensities of the 
 fundamental and the overtones, is to improve or injure its quality 
 according to circumstances. It may be, of course, that the tone 
 desired is a very pure one, or it may be that what is wanted is a
 
 VARIATION IN REVERBERATION 83 
 
 tone with pronounced upi)er purtials. Take, for example, the 
 "night horn" stop in a pipe organ. This is intended to have a very 
 pure tone. The room in contributing to its purity would improve 
 its quality. On the other liand, the mixture stop in a pipe organ is 
 intended to have very pronounced overtones. In fact to tliis end 
 not one but several pipes are sounded at once. The effect of the 
 above room to emphasize the fundamental and to wipe out the 
 overtones would be in opposition to the original design of the stoj). 
 To determine what balance is desirable nuist lie of course with the 
 musicians. The only object of the present series of papers is to 
 point out the fundamental facts, and that our conditions may be 
 varied in order to attain any desired end. One great thing needed 
 is that the judgment of the nuisical authorities should be gathered 
 in an available form; but that is another problem, and tlie above 
 bare outline is intended only to indicate the importance of extend- 
 ing the work to I lie whole nmgc of the musical scale, — the work 
 undertaken in the jjresent paper. 
 
 The method |)uisu('(l in these exjK'riments is not very unlike thai 
 followed in the previous experiments with C4 51'-2. It diti'ers in minor 
 detail. l)ul to explain these details would involve a great deal of 
 repetition which the modifications in the method are not of sufficient 
 importance to justify. 
 
 Rroadly, the procedure consists first in the determination of the 
 rate of emission of the sound of an organ pipe for each note to be 
 investigated. This consists in determining the durations of au<libil- 
 ity after the cessation of two sounds, one having four or more, but 
 a known nmlliple, times the intensity of the other. From these 
 results it is possible to determine the rate of emission by the pipes, 
 each in terms of the iiiinimum audibility for tliat i)articular tone. 
 The a])paratus used in tliis part of tlie experiment is shown in Fig. 1. 
 Four small organs were lixed at a minimum distance of five meters 
 apart. It was necessary to phu'c tlicm at this great distance ajKirl 
 because, as already pointed out, if I'iaced near each other the four 
 sounded logctlicr do not, <'iiiit lour times the sound emitted by one. 
 This wide separation was particularly necessary for the large pipe.-- 
 and the low tones; a very Tuueh less .separation would have .served 
 the i)urpose in the ease of the high tones.
 
 84 
 
 Al{< MIIKC TIUAL .U OUSTICS 
 
 From the point wIuti- tlu- four tuln's Ii-iulinj? to the sinall organs 
 nuH't. a snp!)ly piix- ran. as sliown on the drawing, to an air reservoir 
 in the room l»elo\v. This was f<"(l from an ek-ctrieally driven blower 
 at the far end of tla- l)uihling. Ilu' clironograph was in another 
 room. 'I'lie exi).riinriit> with liiis a|jparatus. hke the experiments 
 
 ^ZM' 
 
 Fig. 1 
 
 lierelofore recorded, were carried out at niglit between twelve and 
 five o'clock. 
 
 The rate of emission of sound by the several pipes having been 
 determined, the next work was the determination of the coefficients 
 of al)sorption. Tlie methods employed having already been suffi- 
 ciently descriheil, only results will be given. 
 
 In the very nature of the problem the most important data is the 
 absorption coefficient of an audience, and the determination of this 
 wjis the first task undertaken. By means of a lecture on one of 
 the recent developments of i)hysics, an audience was enveigled into 
 attending, and at the end of the lecture requested to remain for the 
 experiment. In this attempt the effort was made to determine the 
 coefficients for the five octaves from C2 128 to Ce 2048, including
 
 VARIATION IN REVEIUJKHATION 85 
 
 notes E and (i in cucli octave. For several reasons the experiment 
 was not a success. A threatening' tliuiider storm made the audience 
 a small one, and tiie siiilriness of the almospliere made open win- 
 dows necessary, while the attempt to cover so many notes, thirteen 
 in all, prolonfi;ed the experiment beyond the endurance of the audi- 
 ence. While this experiment failed, another the following summer 
 was more successful. In the year that had elapsed the necessity of 
 carrying the investigation further than the limits intended became 
 evident, and now the experiment was carried from Ci 64 to C7 4()()(), 
 but including (mly the C' notes, .seven notes in all. Moreover, 
 bearing in mind the experiences of the previous sununer, il was 
 recognized that even seven notes would come dangerously near over- 
 taxing the patience of the audience. Inasmuch as the coefficient 
 of absorjjtion for ("4 ol'i had already been determined six years be- 
 fore in the investigations mentioned, the coefficient for this note 
 was not redetermined. The experiment was therefore carried out 
 for the lower three and tiie upper three notes of the seven. The 
 audience, on the night of tiiis experiment, was much larger than 
 that whicli came the previous sununer, the night was a more com- 
 forliil)l<' one, and it was ])ossii)le to close the windows during (lie 
 experiment. 'IMie conditions were thus fairly satisfactory. In order 
 to get as nuich data as possible and in as short a time, there were 
 nine observers stationed at difl'ereni points in the room. These ob- 
 servers, whose kimlness antl skill it is a pleasure to acknowledge, 
 had prepared themselves by i)revious ])ractice for this one experi- 
 ment. As in tlie work of six years ago, the writer's key controlled 
 the organ |)ipes and started the chronograph, the writer and the 
 other observers each had a key which was connecteil with the 
 chronograph to reectid I lie cessation of audibilit_\' of the sound. The 
 results of the exijciiment are shown on the lower curve in Fig. '2. 
 This curve gives the coeilicient of al)sorption ])er ])erson. It is to 
 be ob.served that one of the points fall> clearly otV the smooth curve 
 drawn through the other points. The observations on which this 
 point i> l)ased were, liowexci'. inncli (li>tinli<il by a street car p;iss- 
 ing not far from the building, and the dei)arture of tlii> observation 
 from the ciu-ve does not indicate a real deparlun- in the coefHcient 
 nor should it cast nuich doubt on the ri'>t of the work, in view of the
 
 8G 
 
 ARCHITEC TURAL ACOUSTICS 
 
 circumstances under whicli it was secured. Counteracting the per- 
 haps liad impression whicii this point may give, it is a considerable 
 satisfaction to note how accurately tin- point for C4 512, deter- 
 
 1.0 
 
 
 
 
 
 
 
 .« 
 
 
 / 
 
 
 
 
 
 .H 
 
 / 
 
 / 
 
 
 
 
 
 .7 
 
 / 
 
 
 
 
 
 
 .6 
 
 / 
 
 
 
 
 
 
 .6 
 
 / 
 
 A 
 
 
 
 
 
 
 
 
 .4 
 
 1 
 
 / 
 
 
 
 
 
 .3 
 
 / 
 
 
 
 
 
 
 .2 
 
 I 
 
 
 
 
 
 
 .1 
 
 
 
 
 
 
 
 c, 
 
 c. 
 
 c, 
 
 c. 
 
 c. 
 
 c. 
 
 Fig. 2. The absorbing power of an audience for Jifferent 
 notes. The lower curve represents the absorbing power 
 of an audience per person. The upper curve represents 
 the absorbing power of an audience per square meter 
 as ordinarily seated. The vertical ordinates are ex- 
 pressed in terms of total absorption by a square meter 
 of surface. For the upper curve the ordinates are thus 
 the ordinary coefficients of absorption. The several 
 notes are at octave intervals, as follows: Ci64, GHS, 
 Ci (middle C) 456, C,51i. C61W4, C62048, C7409G. 
 
 mined six years before by a different set of observers, falls on the 
 smooth curve through the remaining points. In the audience on 
 whicii these observations were taken there were 77 women and
 
 \ARIATI()X IX REVP:RBERATI()X 87 
 
 105 iiu'ii. Tlic coiirtt'sy of tin- uuclience in remaining for the ex- 
 periment iiiid I he really remiirkal)le silence wliich they maintained 
 is gratefully acknowledgeil. 
 
 'I'he curve above discussed is that for the average j)erson in an 
 audience. An interesting form in which to throw the results is to 
 regard the audience as one side of a room. We may then look at it 
 as an extended absorbing suriace, and determine the coefficient per 
 square meter. Worked out on this basis the absorption coefficient 
 is indicated in the higher curve. It is merely the lower curve nudti- 
 plied by a nunil)er which expresses the average number of people 
 per s(juare meter. It is interesting to note that the coefficient of 
 absorption is about the same from C4 5^2 up, indicating over that 
 range nearly complete absorption. Below that point there is a very 
 great falling off', down to L\ 04. The curve is such as to permit of 
 an extrapolation indicative of even le.ss absorption and consequently 
 greater reverberation for tiic still lower notes. Wilhout entering 
 into an elaborate discussion of this curve, two points may be noted 
 as i)articularly interesting. The first is the nearly complete absorp- 
 tion for the higher notes, a result which at first sight, seems a little 
 inconsisteiil with the roults which will be shown later on in con- 
 nection with the al)sorptioii i>.v felt. The inconsistency, however, 
 is only apparent. The greater absor])fion shown by an audience 
 than that shown by thick fell arises from the fact that the surface 
 of the audience is irregular and does not result in a single reflection, 
 but |)r()bably, for a very large ])ortion of the sound, of nudtiplt^ re- 
 fli'clion before it finally euiergi's. The physical conditions are such 
 that they ol)viously do not admit of analytic expression, but the 
 explanation of the great absorption by an extended audience sur- 
 face is not (liliicull In nndiTslaiid. In addition to the aboxc lliere 
 is another i)artial explanation which contributes to the results, 
 'i'he felt forms a perfectly continuous niediuni. and therefore offers 
 a comparativi'ly rigid rellecting surface. Tlie comparatively light, 
 thin, and porous nature of the clothing of women, ])erhaps more 
 than of men, contrilmtes to the gi'eat ai>M>r|)linn of the high notes. 
 
 'I'he next ex|)erinu'nt. taking them up <'hronologically, and jmt- 
 hajjs next even from the standi)oint of interest, w;us in regard to a 
 brick wall-surface. This expiriun-nt wjis carried out in the constant-
 
 88 
 
 AUC nil KCTURAL ACOUSTICS 
 
 («-miMTaliirf rcHun iiu-nlioiu-tl in tin- previous papers. The arrango- 
 nu'iit of ai)paralus is sliown in Fig. .'?, wliere the air re.servoir in the 
 room above is sliown in dotted Hnes. In many respects theconstant- 
 tenip«'rature room offered admirable conditions for the experiment. 
 
 ,»f.-.-.is:\i.if-"» 
 
 f^xnU If »^AWt tT.'.'.^.-i i%«'iv.%v» 4 
 
 
 D" 
 
 
 
 Its jjosition in the center of the building and its depth underground 
 made it comparatively free from outside disturbing noises, — so 
 much so that it was possible to experiment in this room in the earlier 
 parts of the evening, although not, of course, when any one else was 
 at work in the building. While it posses.ses these advantages, its
 
 VARIATION IN REVERBERATION 
 
 89 
 
 arched ceiling, by jjlaciiig it in tlie category of special cases, makes 
 extra precaution necessary. Fortunately, at the beginning of the 
 experiment the walls were uni)ainfe(l. Tender these conditions its 
 
 .10 
 .09 
 .08 
 .07 
 .06 
 .05 
 .04 
 .03 
 .02 
 .01 
 
 Z^ZZ 
 
 c. 
 
 c. 
 
 c, 
 
 Fiii. \. The absorbing power of a. 4.5 em. lliiek brick wall. 
 Till' upper curve repre.seiils the ulisorliiiif; power of an 
 iiiipaiiited brick .surface. The bricks were hard but not 
 (jlazeil, and wire set in cement. The hnver curve repre- 
 sents the absi>rl)iiif; power of the same surface painted 
 with two coats of oil paint. The difference between 
 the two curves reprcsinls the absorption due to the 
 porosity of the bricks. In small part, but probably only 
 in snuill part, the dilference is due to diirertucc in super- 
 ficial smoothness. Ct (middle C) iUU. 
 
 coefficient of absorption for difVerent notes was delerniined. It was 
 then painted with an oil paint, two coats, and its coefficient of ab- 
 sorption redetermined. The I wo curves are shown in I'ig. \. The
 
 <)() ARrinTF.f'TrRAT, vroT'STirs 
 
 upiHT curve is for the unpainted brick; the lower curve is that ob- 
 tained after the walls were painted. The difference between the 
 two curves would, if plotted alone, be the curve of absorption due 
 to the j)orosity of the brick. It may seem, perhaps, that the i)aint 
 in covering the bare brick wall made a smoother surface, and the 
 difference between the two results might be due in part to le.ss sur- 
 face friction. ()f course this is a factor, but that it is an exceedingly 
 small factor will be shown later in the discussion of the results on 
 the absorption of sound by other bodies. The absorption of the 
 sounil after the walls are painted is, of course, due to the yielding of 
 the walls under the vibration, to the sound actually transmitted 
 bodily by the walls, and to the absorj)tion in the process of trans- 
 mission. It is necessary to call attention to the fact that the vertical 
 ordinates are here magnified tenfold over the ordinates shown in tlie 
 last curve. 
 
 The next experiment was on the determination of the absorption 
 of sound by wood sheathing. It is not an easy matter to find con- 
 ditions suitable for this experiment. The room in which the absorp- 
 tion by wood sheathing was determined in the earlier experiments 
 was not available for these. It was available then only because the 
 building was new and empty. When these more elaborate experi- 
 ments were under way the room had become occupied, and in a 
 manner that did not admit of its being cleared. Quite a little search- 
 ing in the neighborhood of Boston failed to discover an entirely suit- 
 able room. The best one available adjoined a night lunch room. 
 The night lunch was bought out for a couple of nights, and the ex- 
 periment was tried. The work of both nights was much disturbed. 
 'J'he traffic jjast the building did not stop until nearly two o'clock, 
 and began again about four. The interest of those passing by on 
 foot throughout the night, and the necessity of repeated explana- 
 tions to the police, greatly interfered with the work. This detailed 
 statement of the conditions under which the experiment was tried 
 is made by way of explanation of the irregularity of the observa- 
 tions recorded on the curve, and of the failure to carry this particular 
 line of work further. The first night seven points were obtained for 
 the seven notes Ci 64 to C7 4096. This work was done by means 
 of a portable apparatus shown in Fig. 5. The reduction of these
 
 VARIATION IN REVERBERATION 
 
 91 
 
 results on the following day showed variations indicative of maxima 
 and minima, which to be accurately located would require the de- 
 
 Kio. i 
 
 terminal ion of iuliTnu-dialc i)(>inls. Tin- e.\]H'rinitnl Llic l'i)llo\ving 
 niglil was by means of the organ shown in Fig. G, and points were
 
 92 
 
 AIU HITK( "irRAL ACOUSTICS 
 
 dt'leniiiiu'd for the K aiul G noU's in each octave between Cj l'-28 and 
 Ce 2048. Oilier points would have been determined, but time did 
 not iMTiiiit . It is obvious that the intermediate points in the lower and 
 
 Fig. 6 
 
 in the higher octave were desirable, but no pipes were to be had on 
 such short notice for this part of the range, and in their absence the 
 data could not be obtained. In the diagram, Fig. 7, the points lying 
 on the vertical lines were determined the first night. The points
 
 VARIATIOX IN REVERBERATIOX 
 
 93 
 
 lying between the vertical lines were determined the second night. 
 The accuracy with which these points fall on a smooth curve is 
 
 .12 
 .U 
 
 .10 
 .09 
 .08 
 .07 
 .06 
 .06 
 .04 
 .03 
 .02 
 .01 
 
 / • \ 
 
 / \* 
 
 C, 
 
 c. 
 
 c, 
 
 c. 
 
 c. 
 
 c, 
 
 Flo. 7. Till' iil)sorl)iii>' power of wood .shoalliinK. two centi- 
 nifttT.s thick, Nortli Curoliim pine. Tlic ohservntions 
 were imiili' uikIit wry unsiiiliiblc comlilions. The 
 Hl)Sorptioii is hrrc ilui- almost wholly to yirliliiij; of tht- 
 shrnthin^' us a wholr. thr surface Ix'iii); shellaeked, 
 sinuoth. and iioii-poroiis. The rurve shows one point 
 of resonance- within the ran^je tested, and the proh- 
 nbility of another point of resonance alM>ve. It is not 
 possible now to learn as much in regard to the franiinK 
 and arrangement of lh<- st milling; in the particular room 
 tested as is desirable, d iniiddle ("I ioU.
 
 94 AH( lIITKC'TrRAL ACOUSTICS 
 
 prrliaps all that could he cxpi-cted in view of the difficulty under 
 which the observations were conducted and the limited time avail- 
 able. One jKiint in jjarticular falls far off from this curve, the point 
 for C3 iod, by an amount which is, to say the least, serious, and 
 which can be justified only by the conditions under which the work 
 was done. The general trend of the curve seems, however, estab- 
 lished beyond ri'asoiial)le doubt. It is interesting to note that there 
 is one point of maximum absorption, which is due to resonance be- 
 tween I lie \v;ill> and I lie sound, and that this point of maximum 
 absorjition lies in the lower i)art. though not in the lowest part, of 
 the range of pitch testeil. It would have been interesting to deter- 
 mine, hail the time and facilities permitted, the shape of the curve 
 beyond C7 4096, and to see if it rises indefinitely, or shows, as is far 
 more likely, a succession of maxima. The scale employed in this 
 curve is the same as that employed in the diagram of the unpainted 
 and painted wall-surfaces. It may perhaps be noted in this con- 
 nection that at the very least the absorption is four times that of 
 painted brick walls. 
 
 TliefX])erinu'nt was then directed to the determination of the ab- 
 sorption of sound by cushions, and for this purpose return was made 
 to the constant-temperature room. Working in the manner indicated 
 in tlie earlier papers for substances which could be carried in and 
 out of a room, the curves represented in Fig. 8 were obtained. 
 Curve 1 shows the absorption coefficient for the Sanders Theatre 
 cushions, with which the whole investigation was begun ten years 
 ago. These cushions were of a particularly open grade of packing, 
 a sort of wiry grass or vegetable fiber. They were covered with 
 canviis ticking, and that in turn with a very thin cloth covering. 
 Curve "2 is for cushions borrowed from the Phillips Brooks House. 
 They were of a high grade, filled with long curly hair, and covered 
 with canvas ticking, which was in turn covered by a long nap plush. 
 Curve 3 is for the cushions of Ajipleton Chapel, hair covered with a 
 leatherette, and showing a sharper maximum and a more rapid 
 diminution in absorption for the higher frequencies, as would be 
 expected under such conditions. Curve 4 is probably the most 
 interesting, because for more standard commercial conditions. It 
 is the curve for elastic felt cushions as made by Sperry and Beale.
 
 VARIATION IN REVERBERATION 
 
 95 
 
 It is to be observed thai all four curves fall off for the liiglier fre- 
 quencies, all show a inaxiniuin Kx-ated within an octave, and three 
 
 1.0 
 
 
 
 
 
 
 
 
 
 
 A 
 
 \ 
 
 
 
 
 // 
 
 ^f 
 
 \ 
 
 
 
 
 4 
 
 ^ 
 
 \ 
 
 \ 
 
 '^ 
 
 / 
 
 
 I' 
 
 \ 
 
 \ 
 
 \\ 
 
 / / 
 
 J 
 
 V 
 
 \ 
 
 
 \ 
 
 -A 
 
 7 
 
 
 
 
 \ 
 
 /> 
 
 r 
 
 
 
 
 \ 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 c, 
 
 c, 
 
 c. 
 
 c. 
 
 c, 
 
 Fig. 8. The ahsorhiiij; power of cushions. Curve 1 is 
 for "Sanders Tliealre" cushions of wiry vejjetuble 
 6bcr. covered with canvas tickin;; and a tliin cloth. 
 Curve i is for "Hrooks House" cushions of long hair, 
 covered with the same kind of tickinjj and phish. 
 Curve 3 is for ".Vpplelon Chapel" cushions of hair, 
 covered with ticking and a thin leatherette. Curve 4 
 is for the elastic felt cushions of coninuTce. of elastic 
 cotton. covere<l with ticking and short nap plush. The 
 ab.sorl)ing power is per square meter of surface. 
 Cj (middle C) 2JCi. 
 
 of the curves show a curious hiiinp in I he second ocla\i>. This 
 break in the curve is a genuine pliciioiiienon, as it was tested time 
 after time. It is j)erhai)s <lue to a .secondary resonance, and it is to
 
 96 
 
 AH( IIITEC'l URAL ACOUSTICS 
 
 be observed that it is the more i)ronoimced in those curves that have 
 tlu' sharper resonanee in their jirincipal maxima. 
 
 Observations were llien obtained on unupholstered chairs and 
 settees. The result for chairs is shown in Fig. 10. This curve gives 
 the absorption coefficient per single chair. The effect was surpris- 
 ingly small; in fact, when the floor of the constant-temperature 
 room was entirely covered with the chairs sjxiced at usual seating 
 distances, the effect on the reverberation in the room was exceed- 
 
 FiG. 9 
 
 ingly slight. The fact that it was so slight and the consequent dif- 
 ficulty in mejisuring the coefficient is a partial explanation of the 
 variation of the results as indicated in the figure. Nevertheless it 
 is probable that the variations there indicated have some real basis, 
 for a repetition of the work showed the points again falling above 
 and below the line as in tht- first experiment. The amount that 
 these fell above and below the line was difficult to determine, and 
 the number of points along the curve were too few to justify at- 
 tempting to follow their values by the line. In fact the line is drawn 
 on the diagram merely to indicate in a general way the fact that the 
 coefficient of absorption is nearly the same over the whole range. A 
 varying resonance phenomenon was unquestionably present, but so 
 small as to be negligible; and in fact the whole absorption by the 
 chairs is an exceedingly small factor. The chair was of ash, and its 
 type is shown in tlie accompanying sketch. Fig. 9. 
 
 The results of the observations on settees is shown in Fig. 11. 
 Those plotted are the coefficients per single seat, there being five 
 seats to the settee. The settees were placed at the customary dis-
 
 VARIATION IN RK\'KRBERATK)N 
 
 97 
 
 I ' r c 
 
 tiince. Here again the {)rinfipal interest attaches to the fact that 
 the coefficient of absorption is so exceedingly small that the total 
 effect on the reverberation is hardly noticeable. Here also the 
 plotted results do not fall on the line drawn, and the departure is 
 .03 
 
 .02 
 
 .01 
 
 c. c, a c. C: c. c, 
 
 Fig. 10. The absorbing power of ash chairs shown in Fig. 9. 
 
 (hie i)robably to some slight resonance. The magnitude of the de- 
 parture, however, could not be determined with accuracy because of 
 the small magnitude of the total absorption coefficient. For these 
 reasons and because the number of points was insufficient, no at- 
 
 .03 
 
 .02 
 
 .01 
 
 : ~ ' 
 
 C. 
 
 C, 
 
 c. 
 
 c> 
 
 c. 
 
 c, 
 
 Fig. 11. The ab.sorbiiig power of ash settees shown in 
 Fig. 9. The absorption is per single scat, the settee 
 as shown seating five. 
 
 tem])t was inade lo diMW I he cuinc throiij,'!) the plotted points, but 
 mer("ly to indicate a plotted tendency. The settees were of ash, 
 and their general style is shown in the sketch. 
 
 An investigation was then begun in regard U> I In- nature of I lie 
 process of absorption of .sound. The material chosen for this work 
 was a \rvy durable grade of i'lil. wliicli. as the mamifacturers 
 claimed, was all wool. Kveii a casual examination of its texture 
 makes it difliciilt to believe that it is all wool. It has. however, the
 
 08 AU( Iiri'ECTURAL ACOUSTICS 
 
 advantage of hcing porous, flexible, and very durable. Almost con- 
 stant handling for several years has apparently not greatly changed 
 its consistency. It is to be noted that this felt is not that mentioned 
 in the papers of six years ago. That felt was of lime-treated cow's 
 hair, the kind used in packing steam pipes. It was very much cheai)er 
 in i)rice. but stood little handling before disintegrating. The felt 
 emi)loyed in these experiments comes in sheets of various thick- 
 nesses, the thickness here employed being about 1.1 cm. 
 
 The coefficient of absorption of a single layer of felt was measured 
 for the notes from Cj (>4 to C- 4096 at octave intervals. The experi- 
 ment was repeated for two layers, one on top of the other, then for 
 three, and so on up to six thicknesses of felt. Because the greater 
 thicknesses presented an area on the edge not inconsiderable in 
 comparison with the surface, the felt was surrounded by a narrow 
 wood frame. Tender such circumstances it was safe to assume that 
 the absorption was entirely by the upper surface of the felt. The 
 experiment was repeated a great many times, first measuring the 
 coefficient of absorption for one thickness for all frequencies, and 
 then checking the work by conducting experiments in the other 
 order; that is, measuring the absorption by one, two, three, etc., 
 thicknesses, for each frequency. The mean of all observations is 
 shown in Fig. 12 and Fig. 13. In Fig. 12 the variations in pitch are 
 plotted as abscissas, as in previous diagrams, whereas in Fig. 13 the 
 thicknesses are taken as abscissas. The special object of the second 
 method will appear later, but a general object of adopting this 
 method of plotting is as follows: 
 
 If we consider Fig. 12, for example, the drawing of the line through 
 any one .set of points should be made not merely to best fit those 
 points, but should be drawn having in mind the fact that it, as a 
 curve, is one of a family of curves, and that it should be drawn not 
 merely as a best curve through its own points, but as best fits the 
 whole set. For example, in Fig. 12 the curve for four thicknesses 
 would not have been drawn as there shown if drawn simjjly with 
 reference to its own points. It would have been drawn directly 
 through the points for Ci 64 and C2 128. Similarly the curve for 
 five thicknesses would have been drawn a little nearer the point for 
 C2 128, and above instead of below the point for Ci 64. Considering,
 
 VARIATION IN RE^TRBERATION 
 
 99 
 
 however, the whole family of curves and recognizing that each point 
 is not without some error, the curves as drawn are more nearly 
 correct. The liest method of reconciling the several curves to each 
 
 l.O 
 
 .8 
 
 .4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 /y 
 
 ^ 
 
 
 
 
 / 
 
 // 
 
 / /4/ 
 
 / 
 
 V 
 
 
 
 // 
 
 h\ 
 
 / 
 
 \ 
 
 ^ 
 
 /^ 
 
 // 
 
 1 r 
 
 
 / 
 
 
 / 
 
 ^ / 
 
 7 
 
 /l 
 
 
 
 
 J 
 
 / 
 
 
 
 
 
 y 
 
 J 
 
 
 
 
 
 
 y 
 
 
 
 
 .2 ^ 
 
 C. 
 
 C, 
 
 c. 
 
 c. 
 
 c. 
 
 c, 
 
 Fig. 12. The uhsorbiiig power of fell of (liircrciit thick- 
 nesses. Kach piece of felt was 1.1 cm. in thickness. 
 Curve 1 is for a sint;l<' I hickncss, curve i for two thick- 
 nesses placed one on top of tiie other, etc. As shown 
 by these curves, the absorption is in part by penetra- 
 tion into the pores of the felt, in part by a yicKlin); of 
 the mass as a wliole. Resonance in the latter process 
 is clearly shown by a maximum shiftinj; to lower 
 and lower pitch with increase in thickness of the felt. 
 Cj (middle C; iJU. 
 
 other is to plot two diagram.s, one in which the variations in i)itc]i 
 arc taken as ab.scissa and one in which the variations in thickness 
 of iVlt are taken as abscis.sas; then draw through the points the best
 
 100 ARCHITKCTURAL ACOUSTICS 
 
 fitlinj; curves iind avoraRO flu> com-spoiulinij ordinate's takt-ii from 
 I lit- curves thus drawn; and with lliese average ordinates redraw 
 both families of curves. Tlie points shown on the diagram are of 
 course the original residts obtained experimentally. In general 
 they fall pretty dose to the curves, although at times, as in the 
 j)oints noted, they fall rather far to one side. 
 
 The following will serve to present the points of particular in- 
 terest revealed 1).\ the family of curves in Fig. 12, where the absorp- 
 tion by the several thicknesses is j^lotted against pitch for abscissas. 
 It is to be observed that a single thickness scarcely absorbs the sound 
 from the eight, four, and two-foot organ pipes, Cj 64, C2 l^S, and 
 C3 256, and tlial its al)sorption increases rapidly for the next two 
 octaves, after which it remains a constant. Two thicknesses absorb 
 more — about twice as nnich - for the lower notes, the curve rising 
 more rapidly, passing tliroiigii a maximum between C4 512 and 
 Cs 1024, and then falling off for the higher notes. The same is true 
 for greater thicknesses. All curves show a maximvmi, each succeed- 
 ing one corresponding to a little lower note. The maximum for six 
 thicknesses coincitles pretty closely to C4 512. The absorption of 
 the sound by felt may be ascribed to three causes, — porosity of 
 slructure, compression of the felt as a whole, and friction on the 
 surface. The presence of the maximum must be ascribed to the 
 second of these causes, the compression of the felt as a whole. As 
 to the third of these three causes, it is best to consult the curves of 
 the next figure. 
 
 The following facts are rendered particularly evident by the 
 curves of Fig. 13. For the tones emitted by the eight-foot organ 
 pipe, Ci 64, the absorption of the sound is verj' nearly proportional 
 to the thickness of the felt over the range tested, six thicknesses, 
 (i.6cm. The curves for notes of increasing pitch show increasing 
 value for the coefficients of absorption. They all show that were 
 the thickness of the felt sufficiently great, a limit would be ap- 
 proached — a fact, of course, self-evident — but for C5 1024 this 
 thickness was reached w-ithin the range experimented on; and of 
 course the same is true for all higher notes, Ce 2048 and C7 4096. 
 The higher the note, the less the thickness of felt necessary to pro- 
 duce a maximum effect. The curves of Ci 64, C2 128, C3 256, and
 
 VARIATION IN REVERBERATION 
 
 101 
 
 C4 512, if extended backward, would pass nearly through the origin. 
 
 This indicates that for at least notes of so low a pitch the absorption 
 
 l.O 
 
 .2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 X 
 
 rv 
 
 J\ 
 
 
 
 
 /^ 
 
 J 
 
 / 
 
 / 
 
 
 / 
 
 1 , 
 
 r^ 
 
 / 
 
 
 / 
 
 ?. 
 
 h 
 
 / 
 
 
 / ' 
 
 / 
 
 y 
 
 
 / 
 
 
 / 
 
 
 ^ 
 
 / 
 
 / 
 
 
 ^/ 
 
 ^c, 
 
 
 1 
 
 //■ 
 
 f .^ 
 
 
 
 
 4 
 
 r 
 
 1 
 
 
 
 
 13 3 4 6 6 
 
 Fig. 13. The absorbing power of felt of different tliick- 
 nesscs. The data, Fig. M, is here i)lotte<l in a slightly 
 different manner — horizontally on plotted increasing 
 thickness — and the curves are for notes of different 
 frequency at octave intervals in pitch. Thus plotted 
 the curves show the necessary thickness of felt for 
 practically maxiniuni efhcieney in absorbing sound of 
 different pitch. These curves also show that for the 
 lowest tliree notes surface friction is negligiljle, at leust 
 in comparison with the other factors. For the liigh 
 notes one thickness of felt was too great for the curves 
 to be conclusive in regard lo this point. Ci (middle 
 C) 250. 
 
 of sound would be ziTO, or nearly zero, for zero tliicknoss. Since 
 zero thickness would leave surface effects, the argiuuent leads to
 
 lo-,' ARCIIITKf TrRAL ACOUSTICS 
 
 thi' c-onclusion that surface frictiuii as an agent in the absorption of 
 sound is of small importance. The curves plotted do not give any 
 evidence in lliis respect in regard to the Iiigher notes, €5 1024, 
 Cs ^048, and C7 409G. 
 
 It is of course evident that tlie above data do not by any means 
 cover all the ground that shoidd be covered. It is highly desirable 
 that data should be accessii)le for glass surfaces, for glazed tile sur- 
 faces, for plastered and inii)lastered porous tile, for plaster on wood 
 lalh and plaster on wire lath, for rugs and carpets; but even with 
 these data collected the job would be by no means comi)leted. 
 What is wanted is not merely the measurement of existing material 
 and widl-surfaces, but an investigation of all the po.ssibilities. A 
 concrete case will perhaps illustrate this. If the wall-surface is to 
 be of wood, there enter the cjuestions as to what would be the effect 
 of varying the material, — how ash differs from oak, and oak from 
 walnut or i)ine or whitewood; what is the effect of variations in 
 thickness; what the effect of paneling; what is the effect of the 
 spacing of the furring on wliich the wood sheathing is fastened. If 
 the wall is to be plaster on latli, there arises the question as to the 
 difference between wood lath and wire lath, between the mortar 
 that was formerly used and the wall of today, which is made of hard 
 and im])ervious plaster. What is the effect of variations in thick- 
 ness of the plaster .^ What is the effect of painting the jjlaster in 
 oil or in water colors ? What is the effect of the depth of the air 
 space behind the plaster ? The recent efforts at fireproof construc- 
 tion have resulted in the use of harder and harder wall-surfaces, 
 and great reverberation in the room, and in many cases in poorer 
 acoustics. Is it possible to devise a material which shall satisfj' the 
 conditions as to fireproof qualities and yet retain the excellence of 
 some of the older but not fireproof rooms ? Or, if one turns to the 
 interior furnishings, what type of chair is best, what form of cushions, 
 or what form of upholstery ': There are many forms of auditorium 
 chairs and settees, and all these should be investigated if one pro- 
 poses to apply exact calculation to the problem. These are some of 
 the questions that have arisen. A few data have been obtained 
 looking toward the answer to some of them. The difficulty in the 
 way of the prosecution of such work is greater, however, than ap-
 
 VARIATION IN REVKRHKRA'l'ION 103 
 
 pears at first sight, the; parliciilar diiliciilties being of opportunity 
 and of expense. It is difficult, for i'xanii)le, to find rooms wliose 
 walls are in large measure of glass, especially when one bears in 
 mind that the room must be empty, that its other wall-surfaces 
 must be of a substance fully investigated, and that it must be in a 
 location admitting of quiet work. Or, to investigate the effect of 
 the different kinds of plaster and of the different methods of plaster- 
 ing, it is necessary to have a room, preferably an underground room, 
 which can be lined and relined. The constant-temperature room 
 which is now available for the experiments is not a room suitable 
 to that particular investigation, and for best results a special room 
 should be constructed. Moreover, the expense of plastering and 
 replastering a room — and this process, to arrive at anything like 
 a general solution of the problem, would have to be done a great 
 many times — would be very great, and is at the present moment 
 prohibitive. A little data along some of these lines have been se- 
 cured, but not at all in final form. The work in the past has been 
 largely of an analytical nature. Could the investigation take the 
 form of constructive research, and lead to new methods and greater 
 possibilities, it would be taking its more interesting form. 
 
 The above discussion has been solely with reference to the deter- 
 mination of the coefficient of absorption of sound. It is now pro- 
 posed to discuss the question of the apj)lication of these coefficients 
 to the calculation of reverl)eration. In the first series of papers, 
 reverberation was defined with reference to C4 512 as the continua- 
 tion of the sound in a room after the source had ceased, the initial 
 intensity of the sound being one million times minimum audible 
 intensity. It is debatable whether or not this tlefinition should be 
 extended without alteration to reverberation for other notes than 
 C4 512. There is a good deal to l)e said both for and against its 
 retention. The whole, however, hinges on the outcome of a physi- 
 ological or psychological inquiry not yet in such shape as to lead to 
 a final decision, 'llie ([ucslion is therefore held in abeyance, and 
 for I lie lime the definition is retained. 
 
 Retaining the defiiiilion, I lie reverberation for any pilch can lie 
 calculated bv I lie foruinla 
 
 a
 
 104 ARCHITECTURAL ACOUSTICS 
 
 where V is the vohiine of the room, A' is a constant depending on 
 the initial intensity, and a is the total absorbing power of the walls 
 and the contained material. A' and V are the same for all pitch 
 
 8 
 8 
 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Q 
 
 
 
 
 
 
 
 5 
 
 
 
 
 
 
 
 4 
 
 
 
 
 
 
 
 3 
 
 I 
 
 
 
 
 
 
 2 
 
 V 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c, 
 
 c. 
 
 c. 
 
 Fig. 14. Curves expressing the reverberation in the large 
 lecture-room of the Jefferson Physical Laboratory with 
 (lower curve) and without (upper curve) an audience. 
 These curves express in seconds the duration of the 
 residual sound in the room after the cessation of 
 sources producing intensities 10' times minimum 
 audible intensity for each note. The upper curve de- 
 scribes acoustical conditions which are very unsatis- 
 factory, as the hall is to be used for speaking purposes. 
 The lower curve describes acoustically satisfactory 
 conditions. Cs (middle C) 256. 
 
 frequencies. A is .164 for an initial intensity 10^ times minimum 
 audible intensity. The only factor that varies with the pitch is a, 
 which can be determined from the data given above.
 
 VARIATION IN REVERBERATION 105 
 
 In illustration, the curves in the accompanying Fig. 1-t give the 
 reverberation in the large lecture-room of the Jefferson Physical 
 Laboratory. The upper curve defines the reverberation in the room 
 when entirely empty; the lower curve defines this reverberation in 
 the same room with an audience two-thirds filling the roon). The 
 upper curve represents a condition which would be entirely impracti- 
 cal for speaking purposes; the lower curve represents a fairly satis- 
 factory condition.
 
 MELODY AND THE ORIGIN OF THE MUSICAL 
 
 SCALE" 
 
 In the vice-presidential addresses of the American Association 
 great hititude in the choice of subjects is allowed and taken, but 
 there is, I believe, no precedent for choosing the review of a book 
 printed fifty-five years before. Helmlioltz' Tonenemfinduiujen, pro- 
 duced by a masterful knowledge of jjhysiology, physics, and mathe- 
 matics, and a scholar's knowledge of the literature of music, has 
 warded off all essential criticism by its breadth, completeness, and 
 wealth of detail. Since it was first published it has been added to 
 by the author from time to time in successive editions, and greatly 
 bulwarked by the scholarly notes and appendices of its translator, 
 Dr. Alexander J. Kllis. Tlic original text remains unchanged, and 
 unchallenged, ;xs far as physicists are concerned, in all important 
 respects. In taking exception at this late day to the fundamental 
 thesis of Tart III, I derive the necessary courage from the fact that 
 should such exception be sustained, it will serve to restore to its 
 full application that greater and more original contribution of Helm- 
 holtz which he included in Part II. Having given a physical and 
 physiological explanation of the harmony and discord of simul- 
 taneous sounds, and, therefore, an explanation of the musical scale 
 as used in modern composition, Ilelmholtz was met by an apparent 
 anachronism. The musical scale, identical with the modern musi- 
 cal scak' in all essentials, antedated by its use in single-jiart melody 
 the invention of chordal comi)osition, or, as Ilelmholtz expressed 
 it, preceded all experience of musical harmony. In .seeking an ex- 
 planation of this early invention of the musical scale, Ilelmholtz 
 abandoned his most notable contribution, and relegated liis expla- 
 nation of harmony and discord to the minor service of explaining 
 a fortunate, though of course an important use of an already in- 
 vented system of musical notes. The explanation of the original 
 
 * Vice-Presidential .\ddress. Section B, American .\ssociBlion for tin- .Vdvanccnicnl of 
 Science, Chicago, 1907. 
 
 107
 
 108 MELODY 
 
 invention of the musical scale and its use in single-part music 
 Ihrouph the classical and the early Christian eras, he sought for 
 in i)urely aestlietic considerations, — in exactly those devices from 
 wliich he had just succeeded in rescuing the explanation of harmony 
 and discord. 
 
 The liunian ear consists of three parts, — in the nomenclature 
 of anatomy, of the outer, niitldle, and inner ear. The outer and 
 the inner ears are connected by a series of three small bones trav- 
 ersing the middle ear and transmitting the vibrations of sound. 
 'I'lie inner ear is a peculiarly shai)ed cavity in one of the hard bones 
 of tlie skull. That i)art of the cavity with which we are here con- 
 cerned is a long passage called from its resemblance to the interior 
 of a snail shell the cochlea. The cavity has two windows which are 
 closed by membranes. It is to the uppermost of these membranes 
 that the train of three small bones, reaching from the drum of the 
 outer ear, is attached at its inner end. It is to this upper membrane, 
 therefore, tluit tiio vibration is communicated, and through it the 
 \ibration reaches the fluid which fills the inner cavity. As the 
 membrane covering tlie ui)per window vibrates, the membrane 
 covering the lower window yielding, also vibrates, and the motion 
 of the fluid is in the nature of a slight displacement from one to 
 the other window, to and fro. From between these windows a dia- 
 phragm, dividing the passageway, extends almost the whole length 
 of the cochlea. This diaphragm is composed in part of a great 
 number of very fine fibers stretched side by side, transverse to the 
 cochlea, and called after their discoverer, fibers of Corti. On this 
 diaphnigm terminate the auditory nerves. ^Mien the liquid vibrates, 
 the fibers vibrate in unison, the nerve terminals are stimulated, and 
 thus the sensation of sound is produced. These fibers of Corti are 
 of different lengths and presumably are stretched with different 
 tensions. They therefore have different natural rates of vibration 
 and a sympathetic resonance for different notes. The whole has 
 been called a harp of several thousand strings. 
 
 Were these fibers of Corti verj' free in their vibration, each 
 would respond to and would respond stronglj^ only to that partic- 
 ular note with whose frequency it is in unison. Because of the fact 
 that they are in a liquid, and possibly also because of the manner
 
 ORIGIN OF THE MUSICAL SCALE 109 
 
 of their terminal connections, they are considerably damped. Be- 
 cause of this their response is both less in amount and less selective 
 in character. In fact, under these conditions, not one, but many 
 fibers vibrate in n-sjjonse to a single pure note. A considerable 
 length or area of tlie diaphragui is excited. So long as the exciting 
 sound remains pure in (iualit.\-. constant in pitch, and constant in 
 intensity, the area of the diaphragm affected and the amplitude of 
 its vibration remain imchanged. If, however, two notes are sounded 
 of nearly the same pitch, the areas of tiie diaphragm affected by the 
 two notes overlap. In tiic ()Vi'riapi)ing regitm the vil)rati()n is violent 
 when the two notes are in the same phase, weak when they are in 
 opposite phase. The result is the familiar jihenomena of beats. 
 Such beats when slow are not disagreeable and not without musical 
 value. If the difference between the two notes is incre;ised, the 
 beats become more rapid and more disagreeable. To this violent 
 disturbance, to the starling and stopping of the vibration of the 
 fibers of Corti, Ilclniholtz ascribed the sense of roughness which we 
 call discord. As tlu' notes are more widely separated in ])itch, the 
 overlai)ping of the affected areas (liiiiiuislies. Between pure notes 
 the sense of discord disappears willi suliiciint. separation in pitcli. 
 When the two vibrating areas exactly match, because the two notes 
 are of exactly the same pitcli, and when the two areas do not in the 
 least overlap, because of a sufficiently wide separation in pitch, the 
 result according to Hehnholtz is harmony. Partial overlajiping of 
 the affected areas produces beats, and the roughness of beats is 
 discord. Such, reduced to its fewest elements, is Hehnholtz' expla- 
 nation of the harmony and discord of tones which are pure. 
 
 J{ul no nuisical tone is simjjle. It always consists of a combina- 
 tion of so-called partial tones which l)ear to eacli other a more or 
 less simple relationship. Of these partial tones, one is called the 
 fuudaniental, — .so-called i)ecause it is the loudest or lowest or, 
 better still, becau.se it is thai to which the oilier partial tones bear 
 the simjilest relation. A nmsical tone, therefore, affects not one, 
 bill. Ilirougli its fundamental and ujjper partial toiieS, several areas 
 of the diaphragm in the cochlea. Two niusiral tones, each with its 
 fiindanuntal and upper parlials. Ilu-refore. affect areius of the dia- 
 phragm which overlap each other in a more or less complicated
 
 110 MELODY 
 
 iiianncr, (It'ix'ndinf; dii tlic relative frequencies of tlie fundamentul 
 tones and the relationships of tlieir upper partials. The exact 
 matching of the arejis affected by these two systems of partial tones, 
 or the entire separation of the affected areas, give luirmony. The 
 overhii)i)ing of these affected areas, if great, prochices discord, or. if 
 slight in amount, modifications and color of harmony. 
 
 In the great majority of musical tones the upper partials bear 
 simple relationships to the fundamentals, being integral multiples 
 in vibration frequency. Helmlioltz showed that if of two such 
 tones one continued to sound unchanged in pitch, and the other 
 starting in unison was gradually raised in pitch, the resulting dis- 
 cord would pass through maxima and minima, and that the minima 
 would locate the notes of the pentatonic scale. The intermediate 
 notes of the complete modern musical scale are determined by 
 a repetition of this process starting from the notes thus deter- 
 mined. 
 
 If to this is added a similar consideration of the mutual inter- 
 ference of the combinational tones which are themselves due to 
 the interaction of the partial tones, we have the whole, though of 
 course in the briefest outline, of Helmlioltz' theory of the harmony 
 and discord of simultaneously sounding musical tones. 
 
 Having thus in Parts I and II developed a theory for the har- 
 mony and discord of simultaneous sounds, and having developed 
 a theory which explains the modern use of the musical scale in 
 chords and hannonic music, Helmlioltz pointed out, in Part III, 
 tliat the musical scale in its present form existed before the inven- 
 tion of harmonic music and before the use of chords. 
 
 Music may be divided into three principal periods : — 
 
 1. "Homophonic or Unison Music of the ancients," including the music 
 
 of the Christian era up to the eleventh century, " to which also 
 belongs the existing music of Oriental and Asiatic nations." 
 
 2. "Polj-phonic music of the middle ages, with several parts, but with- 
 
 out regard to any independent musical significance of the har- 
 monies, extending from the tenth to the seventeenth centurj'." 
 
 3. "Hannonic or modern music characterized by the independent 
 
 significance attributed to the harmonies as such."
 
 ORIGIN OF THE ^^'SI^AL SCALE 111 
 
 Polyphonic music was the first to cull for the production of 
 simultaneous sounds, and, therefore, for the hearing or the experi- 
 ence of musical harmony. Homophonic music, tliat which alone 
 existed up to the tenth or eleventh century, consisted in tiie pro- 
 gression of single-part melody. Struck by this fact, Ilelmholtz 
 recognized the necessity of seeking another explanation for tiie 
 invention and the use of a scale of fixed notes in the music of this 
 period. To borrow his own words, "scales existed long before 
 there was any knowI(>dge or experience of hannony." Again, else- 
 where, he says in emphasizing the point: "Tlie indi\idual parts of 
 melody reach the ear in succession. We cannot perceive them all 
 at once; we cannot observe backwards and forwards at pleasure." 
 Between sounils [)roduced and heard in discrete succession, there 
 can be neither harmony nor discord, there cannot be beats, or 
 roughness or interruption of continuous vibrations. Regarding the 
 sounds of a melody as not merely written in strict and non-over- 
 lapping succession, but also as produced and heard in discrete suc- 
 cession, Hclmholtz sought another b;usis for the choice of the notes 
 to constitute a scale for homophonic music. His explanation of 
 this invention can be best presented l)y a lew (juotations: — 
 
 Melody has to esqjress a motion in siu-li a inamicr that the hearer may 
 easily, clearly, and certainly appreciate tlie eliaracter of tliat motion hy 
 iininediale i)erce])ti()n. This is only possible wiieii the steps of tiiis motion, 
 their rapidity, and tiicir amount, are also exactly measurable by immediate 
 sensible ]K'rcei)ti<)n. Melodic motion is ciiaiige of j)itch in time. To meas- 
 ure it perfectly, the lenfjlli of time elapsed and llie tlistanee between the 
 pitches must be measurable. This is possible for immediate audition only 
 on condition that the alterations both in time and pitch should proceed by 
 regular and dclcrniiiiate degrees. 
 
 Again Hclniiiollz says: — 
 
 For a clear and sure measurement of tlie change of pitch no means was 
 left but progression by determinate degrees. This scries of degrees is laid 
 down in the musical scale. When the wind howls and its pitch rises or falls 
 in insensible gradations without any break, we have nothing to measure 
 the variations of pitch, nothing by which we can compare the later with the 
 earlier sounds, and comprehend the extent of the change. The whole phe- 
 nomenon i)r(>(hices a confused, unpleasant impression. The nnisical scale 
 is as it were the divided rod, by which we measure progression in pitch, as 
 rhythm measures progression in time.
 
 Ibi MKLODY 
 
 I^ter lie says: — 
 
 Lot us begin with the Octave, in which the relationship to the funda- 
 mental tone is most remarkable. I^t any melody be executed on any in- 
 strument which has a good musical quality of tone, such as a human voice; 
 the hearer must have heard not only the primes of the compound tones, but 
 also their upf)er octaves, and. less strongly, the remaining upper partials. 
 When, then, a higher voice afterwards executes the same melody an Octave 
 higher, we hear again a part of what we heard before, namely the evenly 
 iiiiml)ered i)artial tones of the former compound tones, and at the same 
 time we hear nothing that we had not jjreviously heard. 
 
 AVhat is true of the Octave is true in a less degree for the Twelfth. 
 If a melody is repeated in the Twelfth we again hear only what we had 
 already heard, but the repeated part of what we heard is much weaker, 
 because only the third, sixth, ninth, etc., partial tone is repeated, whereas 
 for re])etition in the Octave, instead of the third partial, the much stronger 
 .second and weaker fourth partial is heard, and in place of the ninth, the 
 eighth and tenth occur, etc. 
 
 For the repetition on the Fifth, only a part of the new sound is iden- 
 tical with a part of what had been heard, but it is, nevertheless, the most 
 perfect repetition wliicl) can be executed at a smaller interval than an 
 Octave. 
 
 ^Vithout carrying these quotations further they will sufRce to 
 illustrate the basis which Helmholtz would ascribe to homophonic 
 music and early melodic composition. On this explanation the 
 basis of melody is purely that of rhythm and rhythm based on a 
 scale of intervals. The scale of intervals in turn is based on a 
 recognition, conscious or subconscious, of the compound character 
 of nnisical tones, and of the existence in tones of different pitch of 
 l>artials of the same pitch. This calls for a degree of musical in- 
 sight and discrimination which it is difficult to credit to a primitive 
 art. It is in reality the skill of the highly trained musician, of a 
 musician trained by long experience with sounds which are rich 
 and accurate in quality. This power of analysis goes rather with 
 supreme skill than with the early gropings of an art. 
 
 MWr liaving developed a theory of harmony and discord based 
 on elaborate experimental and mathematical investigations, which 
 was remarkable in bringing together three such diverse fields as 
 physics, physiology, and aesthetics, he relegated it to the minor 
 ajjplication of explaining the use in modern music of an already
 
 ORIGIN OF THE MUSICAL SCALE 113 
 
 existing and highly developed musical scale, and sought an expla- 
 nation of the earlier use of the scale in melody and its original in- 
 vention in the principle which is very far from possessing either 
 the beauty or the convincing (juality of his earlier hypothesis. He 
 was forced to this by a i^riorily of melodic or homophonic compo- 
 sition. He saw in melody only a succession of notes, no two exist- 
 ing at the same time, and therefore incapable of producing harmony 
 or discord in a manner such as he had been considering. 
 
 It is true that melody is written as a pure succession of discrete 
 notes, one beginning only when the otlier has cetised. It is true also 
 that melody is so sung and so produced on a homophonic instru- 
 ment, such as the voice, flute, reeds, or one-stringed instruments. 
 This is peculiarly true of the voice, and it is with the voice that 
 one naturally associates the earliest invention of the .scale. But 
 while it is true that the earliest song must have consisted of tones 
 produced only in succession, it is not necessarily true tliat such 
 sounds were heard as isolated notes. A sound produced in a space 
 which is in any way c-onfined continues until it is diminished by 
 transmission tlirou^Mi ojx-nings or is absorbed by the retaining walls, 
 or contained iiiatcriai to such a point tliat it is past llic threshold 
 of audibility, and this prolongation of audibility of sound is under 
 many conditions a factor of no inc()nsi(leral)le iiniiortance. In many 
 rooms of ordinary construction the prolongation of audibility 
 amounts to two or three seconds, and it is not exceedingly rare that 
 a sound of moderate initial intensity should continue audible for 
 eight, nine, or ev'en ten seconds after the source has ceiised. As a 
 result of this, single-part nuisic produced as successive separate 
 sounds is, nevertheless, heard as overlapi)ing, and at times as greatly 
 overlaj)j)ing tones. Each note maj* well be audible with appreciable 
 intensit\- not incrcly through the next. Itut through several suc- 
 ceeding notes. I lulcr such conditions we iiave every opportunity, 
 even with single-i)arl nuisie, for llu- production of all the |)lR'noiiiena 
 of harmony and discord which has been discussed by Helmholtz in 
 explanation of the cliorilal nse of llu- iiiiisical scale. In any ordi- 
 narily bare and uncari)eled room, one may sing in succession a 
 .series of notes and thru hear for .some time afterward their full 
 ehordal etlVcl.
 
 lU MELODY 
 
 All the arpiimonts that Ilelmholtz advanced m support of his 
 iiypothi'sis. that the nuisical scale was devised solely from con- 
 siderations of rliythm and founded on a repetition of faint upper 
 partials, hold with equal force in the explanation here proposed. 
 The identity of jiartial tones in compound tones with different 
 fundamentals is one of the conditions of harmony, antl the scale 
 devised by considerations of the mutual harmony of the notes 
 sounded simultaneously, would, in every respect, be the same as 
 that of a scale based on repeated upper partials. In the one case 
 the identity of upper partials is an act of memory, in the other it 
 is determined by the harmony of sustained tones. All the argu- 
 ments by Helmholtz based on historical considerations and on 
 racial and national differences are equally applicable to the hy- 
 pothesis of sustained tones. In fact, they take on an additional 
 significance, for we may now view all these differences not merely 
 in the light of differences in racial development and temperament, 
 but in the light of physical environment. Housed or unhoused, 
 dwelling in reed huts or in tents, in houses of wood or of stone, in 
 houses and temples high vaulted or low roofed, of heavy furnish- 
 ing or light, in these conditions we may look for the factors which 
 determine the development of a musical scale in any race, which 
 determine the rapidity of the growth of the scale, its richness, and 
 its considerable use in single-part melody. 
 
 The duration of audibility of a sound depends on its initial in- 
 tensity and on its pitch, to a small degree on the shape of the con- 
 fined space, and to a very large degree on the volume of the space 
 and on the material of which the walls are composed. The duration 
 of audiijility is a logarithmic function of the initial intensity, and 
 as the latter is practically always a large multiple of the minimum 
 audible intensity, this feature of the problem may be neglected 
 when considering it broadly. For this discussion we may also leave 
 out of consideration the effect of shape as being both minor and too 
 intricately variable. The pitch here considered will be the middle 
 of the musical scale; for the extremes of the scale the figures would 
 be very different. The problem then may be reduced to two factors, 
 volume and material. It is easy to dispose of the problem reduced 
 to these two elements.
 
 ORIGIN OF THE MUSICAL SCALE 115 
 
 The duration of audibilily of a sound is directly proportional to 
 the volume of a room and inversely proportional to the total ab- 
 sorbing power of the walls and the contained material. The volume 
 of the room, the shape remaining the same, is proportional to the 
 cul)e, while the area of tlic walls is proportional to the square of 
 the linear dimensions. The duration of audibility, proportional to 
 the ratio of these two, is proportional to the first power of the linear 
 dimension. Other things being equal, the duration of audibility, 
 the overlapping of successive .sounds, and, therefore, the experience 
 of harmony in single-part music is proportional to the linear di- 
 mensions of the room, be it dwelling house or temple. 
 
 Turning to the question of material the followmg figures are 
 suggestive: Any opening into the outside space, provided that 
 outside space is itself unconfined, may be regarded as being totally 
 absorbing. The absorbing jiower of hard pine wood sheathing 
 of one-half inch thickness is 6.1 per cent; of plaster on wood lath, 
 3.4 per cent; of single-thickness glass, 2.7 per cent; of brick in 
 Portland cement, 2.5 per cent; of the same brick painted with oil 
 paint, 1.4 percent. Wood sheathing is nearly double any of the 
 rest. On the other hand, a man in the ordinary clothing of today 
 is equal in liis absorbing power to nearly 48 per cent of that of a 
 square meter of unobstructed opening, a woman is 54 per cent, and 
 a square meter of audience at ordinary seating distance is nearly 
 90 JHT cent. Of significaiue also in this connection is the fact that 
 Oriental rugs have an absorbing power of nearly 29 per cent, and 
 house plants of 11 percent. 
 
 Of course, the direct a])i)licalion of these figures in any accurate 
 calculation of the conditions of life among different races or at dif- 
 ferent jieriods of time is inijjossible, but they indicate in no uncer- 
 tain manner tiie great differences acoustically in the environment 
 of Asiatic races, of aboriginal r.ices in central and southern Africa, 
 of the Mediterranean countries, of northern Eurojje at different 
 periods of time. NVe have ex|)hiiiud for us by these figures why the 
 nnisical scale hiis but slowly develojx'd in the greater part of Asia 
 and of Africa. .Vlniost no traveler has reported a nnisical .scale, 
 even of the most primitive sort, among any of the ])reviously un- 
 visiled tribes of Africa. This fad could not be aseril)ed to racial
 
 11 (J MELODY 
 
 inapt ilw(K'. If im-lody was, as Ilelnilioltz suggested, but rhythm in 
 time and in pitch, the musical scale should have been developed in 
 Africa if anywhere. These races were given to the most rhythmical 
 dancing, and the rhj^hmical beating of drums and tomtoms. 
 Rhythm in time they certainly had. ^Moreover, failure to develop 
 a musical scale could not be ascribed to racial inaptitude to feeling 
 for pitch. Transported to America and brought in contact with 
 the musical scale, the negro became immediately the most musical 
 part of our poi)ulation. The absence of a highly developed scale in 
 Africa nuist then be ascribed to environment. 
 
 Turning to Eiu"ope we find the musical scale most rapidly de- 
 veloping among the stone-dwelling people along the shores of the 
 Mediterranean. The development of the scale and its increased 
 use kept pace with the increased size of the dwellings and temples. 
 It showed above all in their religious worship, as their temples and 
 churches reached cathedral size. The reverberation which accom- 
 panied the lofty and magnificent architecture increased until even 
 the spoken service became intoned in the Gregorian chant. It is 
 not going beyond the bounds of reason to say that in those churches 
 in Europe which are housed in magnificent cathedrals, the Catholic, 
 the Lutheran, and Protestant Episcopal, the form of worship is in 
 part determined by their acoustical conditions. 
 
 This presents a tempting opportunity to enlarge on the fact 
 that the alleged earliest evidence of a musical scale, a supposed 
 flute, belonged to the cave dwellers of Europe. This and the im- 
 pulse to sing in an empty room, and the ease with which even the 
 unmusical can keep the key in simple airs under such conditions, 
 are significant facts, but gain nothing by amplification. The same 
 may be said of the fact that since music has been wTitten for more 
 crowded auditoriums and with harmonic accompaniment melody 
 has become of less harmonious sequence. These and many other 
 instances of the effect of reverberation come to mind. 
 
 In conclusion, it may not be out of place to repeat the thesis 
 that melody may be regarded not only as rhythm in time and 
 rhythm in pitch, but also as harmony in sustained tones, and that 
 we may see in the history of music, certainly in its early beginnings, 
 but possibly also in its subsequent development, not only genius 
 and invention, but also the effect of physical environment.
 
 ARCHITECTURAL ACOUSTICS^ 
 EFFECTS OF AIR CURRENTS AND OF TEMPERATIRE 
 
 V/RDiXAUiLY there is not :i close connection between the flow of 
 air in a room and its acoustical properties, although it has been fre- 
 quently suggested that thus the sound may be carried effectively 
 to different parts. On the other hand, while the motion of the air 
 is of minor importance, the distribution of temperature is of more 
 importance, and it is on reliable record that serious acoustical diffi- 
 culty has arisen from abrupt differences of temperature in an audi- 
 torium. Finally, transmission of disturbing noises through the 
 ventilation ducts, jjcrhaps theoretically a side issue, is practically 
 a legitimate and necessary jiart of the subject. The discussion will 
 be under these three heads. 
 
 The first of the above three topics, the possible eflFect of the mo- 
 tion of the air on the acoustical property- of a room, is the immediate 
 subject . 
 
 Ventilation 
 
 It was suggested during the jilanning of the Boston Symphony 
 Hall that its acoustical properties would be greatly benefited by 
 introducing the air for ventilation at the front and exhausting at 
 the back, thus carrying the sound by the motion of the air the length 
 of the room. The same suggestion has been made to the writer by 
 others in regard to other buildings, but this case will serve ius suffi- 
 cient example. The suggestion was unoflicial and the gentleman 
 proi)osing it accompaniicl it by a section of a very different hall from 
 the hall designed by Mr. McKim, but as this section was only a 
 sketch and without dimensions the following calculation will be 
 made as if the idea were to be applied to the present hall. It will 
 be shown that the result thus to be secured, while in the right 
 
 ' Engineering HcconI, .Juih', lOUt. 
 IIT
 
 lis ARCHITECTURAL ACOUSTICS 
 
 direction, is of a magnitude too small to be appreciable. To make 
 this the more decisive we shall assume throughout the argument 
 the most favorable conditions possible. 
 
 If a sound is produced in still air in open space it spreads in a 
 sjjherical wave diminishinf^ in intensity as it covers a greater area. 
 The area of a sphere being i)roportioned to the square of the radius, 
 we arrive at the common law that the intensity of sound in still air 
 is inversely proportional to the square of the distance from the 
 source. If in a steady wind the air is moving imiformly at all alti- 
 tudes, the sound still spreads spherically, but with a moving center, 
 
 Fig. 1 
 
 the whole sphere being carried along. If the air is moving toward 
 the observer, the sound reaches him in less time than it otherwise 
 would, therefore spread over a less spherical surface and louder. 
 If, on the other hand, the observer is to windward, the sound has 
 had to come against the wind, has taken a longer time to reach him, 
 is distributed over a greater surface, and is less loud. 
 
 The three cases are represented in the accompanj^ing diagram. 
 The stationary source of sound being at S, a is the wave in still air 
 arriving at both observers at the same time and with the same in- 
 tensity. If the air is moving to the left, the center of the wave will 
 be shifted by an amount d to the left while the wave has spread to 
 Oi. On arrival it will have the size h, less than a, and will be louder. 
 On tlie other hand, while the wave is reaching 02, the observer to 
 windward, the center will have been shifted to the left by an even 
 greater amount ^2- In this case the size of tlie wave will be c, larger 
 than a, and the sound will be less. The loudness of the sound in the 
 three cases is inversely as the three surfaces a, b, and c. If the dis-
 
 b 
 
 EFFECTS OF AIR CITRREXTS 119 
 
 tance of tlie observer Iroin S is denoti-d by r, the loudness of the 
 sound in the three cases will be as 
 
 1 1 ■ 1 
 
 The above result iiuiy lie expressed in the following nioic simple 
 and practical form. II', in the diagram, a is lli<- wave in still air, it 
 corresponding position wiieii of the same size and, therefore, of the 
 same intensity in moving air will he a', the movement of the air 
 having been sufficient to carry the wave a distance d while it has 
 expanded witii the velocity of sound to a sphere of radius r. The 
 distance d and the radius r are to each other as the velocity of wind 
 and the velocity of sound. If thi> observers o, and Oo move, the one 
 away from the source and the other toward it, by a distance d, the 
 sound will be of the same intensity to both as in their first positions 
 in still air. 
 
 In order to make ajjplication of this to the particular problem 
 in hand, we shall assume a normal air su])ply to the room for ven- 
 tilation i)urposes of one-sevciitictli of a culjic meter per person per 
 second. This, if intiodnccd all at one end and exhausted all at the 
 other, in a room 17.9 meters high, 'i'i.H meters broad, and seating 
 about '■2()()() persons, would produce a velocity of the air of 0.09 
 meters per second, assuming the velocity to be the same at every 
 point of a transverse .section. Leaving out of account the ques- 
 tionable merits of this arrangement from the ventilation standpoint, 
 its acoustical value can be calculated readily. 
 
 The velocity of sound under normal conditions being about 
 340 meters per second, the time required to traverse a hall 40 meters 
 long is only about one-ninth of a second. In tiiis short inler\al of 
 time the motion of the air in the room, due to the ventilation, would 
 be sufficient to advance the sound-wave only 0.01 meters, or one cen- 
 timeter. It would thus arrive at the liaek of the room ius a sphere 
 with its center one centimeter nearer than t he source. That is to saj', 
 the beneficial effect of this proposed system of ventilation, greatest 
 for the auditor on the rear seal, would to him be equivalent at the 
 very maxinuun to bringing the stage into the room one centimeter 
 further, or it would be equivalent to bringing the auditor on the
 
 Ui) ARCHITKCrrRAL ACOUSTICS 
 
 rear scat forward ono centimeter. This distance is so sli^lit tiiat 
 without niovinf,' in Ids seat, in fact, without moving his shoulders, 
 a slipiit inclination of the liead would accomplish an equivalent 
 gain. Thvis, while the effect is in the right direction, it is of entirely 
 iMii)ercei)til»le magnitude. If we take into account the sound re- 
 flected from walls and ceiling, the gain is even less. 
 
 Hut the suggestion which is the text of the present paper was 
 not made by one, but by several gentlemen, and is based on the 
 well-recognized fact that one can hear better, often very much 
 better, with the wind than against it, and better than in still air. 
 Therefore, the suggestion is not groundless and cannot be disposed 
 of tlius summarily, certainly not witliout submitting to the same 
 calculation the out-of-door experience that gave rise to the thought. 
 
 In llu' nomenclature of the United States Weather IJureau a 
 wind of from "1 to 5 miles an hour is called light, 6 to 14 miles 
 fresh, 15 to 24 miles brisk, 25 to 37 miles high, and a wind of from 
 40 to 59 miles is called a gale." Taking the case of a "high wind" 
 as a liberal example, its average velocity is about 14 meters per 
 second, or about one twenty-hfth the velocity of sound. In such 
 a wind the sound 1000 meters to leeward would be louder than in 
 still ;iir only by an amount which would be equivalent to an ap- 
 proach of 40 meters, or 8 per cent. Similarly, to windward the sound 
 would b(> less loud by an amount equivalent to increasing the dis- 
 tance from 1000 to 1040 meters. This is not at all conniiensurate 
 with general experience. The difference in audibility, everyone w ill 
 agree, is generally greater and very much greater than this. The 
 discre])ancy, however, can l^e explained. The discrepancy is not 
 between observation and theory, but between observation and a 
 very incomplete analysis of the conditions in the out-of-door ex- 
 perience. Thus, the ordinary view is that one is merely hearing 
 with or against the wind and this wand is thought of as steady and 
 uniform. As a matter of fact, the wind is rarely steady, and partic- 
 ularly is it of different intensity at different altitudes. Fortunately, 
 the out-of-door phenomenon, which in reality is very complex, has 
 been carefully studied in connection with fog signals. 
 
 The first adequate ex-planation of the variation in loudness of a 
 sound with and against the wind was by the late Sir George G.
 
 EFFECTS OF AIR CT'RREXTS 121 
 
 Stokes in an article "On the Eft'ect of Wind on the Inten.sit\- of 
 Sound," in the Report of the Brititih Association for the Advancement 
 of Science for 1857. The complete paper is as follows: 
 
 The reinarkiihk' (liinimilioii in tlic intensity of sound, wliicli is produced 
 when a slroiij; wind Mows in a direction from tlie ol)server toward the 
 source of sound, is familiar to everyhody, hut has not liitlierto heen ex- 
 plained, so far as I lie Miidmr is aware. At first sight we might he disposed 
 to attriltute it merely to t lie increase in the radius of the sound-wave wliieh 
 reaches tiie ohserver. The whole mass of air heini,' su])])osed to he carried 
 uniformly along, the time which the sound would take to reach the ol>- 
 .server, and conse(|uently the radius of the sound-wa\-e would he increased 
 hy the wind in the ratio of the \clocity of souiul to the smn of the velocities 
 of sound and of the wind, and the intensity would he diminished in the 
 inverse du])licate ratio. Hut the t H'ect is nuieh too great to he attril>utal)le 
 to this cause. It woulii he a strong wind whose velocity was a twenty- 
 fourth part of that of soun<l; yet e\eii in this case the intensity wnuM l)e 
 diminished hy only ahout a twelfth ])art. 
 
 The first \-olume of the Aiiiialr.s tie Chimie (1816) contains a |)aper 
 hy M. Delaroclic, giving the ri-sults of some experiments nuide on this 
 suhject. It appeared from the experiments, first, that at small distances 
 the wind has hardly any |)erceptil)le cit'cct, the sound heing propagated 
 almost equally well in .-i (lirectidn conlrary to llic wind .ind in (he direction 
 of the wind; second, that the disi)arity hetwcen the intensity |)ro|)agateti 
 in these two directions I)e<'omes proportionally greater and greater as the 
 distance increases; third, that soun<l is jirojiagated rather liettcr in a direc- 
 tion ])er])endicular to the wind than even in the direction of the wind. The 
 ex])lanation offered hy the author of the present conununication is as 
 follows : 
 
 If we imagine the wlioh- mass of air in the neighhorhood of the source of 
 disturhancc di\ided into horizontal strata, these strata do not move with 
 the .same \cl(icily. Tlu- lower strata arc retarded hy friction against the 
 earth and hy the various ohstacles they meet with; the upper hy fri<-tion 
 against the iow<-r, and so on. Hence, the velocity increas<'s from the 
 ground ui)ward, conformalily with oh.servation. This increa.se of velocity 
 disturhs the spherical form of the sound-wave, tending to make it M>me- 
 wliat of the form of an ellipsoid, the se<-tion of which hy a \'ertii-al diametral 
 ])lanc parallel to thi' direction of the winil is an ellipse meeting the ground 
 at an ohtuse angle on the side towards which th<- wiriil is hlowing, and an 
 acute angle on the opposite side. 
 
 Now, sound tends to projiagate it.self in a direction iHTpendiiular to tin- 
 sound-wave; and if a |)orlion of the wave is intercepted l>y an oiotai-je of 
 larger size the .space Iwhind is left in a .sort of .snund-shadow, and the only
 
 li^i ARCHITECTITIAL ACOUSTICS 
 
 sound tluTc lit-aril is wliat tiiverges from the {general wave after i)assin<r 
 till' olislaclo. Uriice. near tlio oarlli. in a dirfctioii contrary to the wind. 
 the soiiiul continually tends to I)c i)ropaf,'ated ui)\vards, and consequently 
 there is a eontiiuial ten<lenoy for an ol)server in tliat direction to be loft in 
 a sort of sound-slia<lo\v. Hence, at a sufKcient distance, the sound ought 
 to he \ery much enfeebled; but near the source of disturbance this cause 
 has not yet had time to operate, and, therefore, the wind produces no 
 sensil)le effect, exce|)t wiiat arises from the augmentation in tlie radius of 
 the .sound-wave, and this is too small to be perceptible. 
 
 In the contrary direction, that is, in the direction towards which the 
 wind is blowing, the sound tends to propagate itself downwards, and to be 
 reflected frotn the surface of the earth; and both the direct and reflected 
 waves contribute to the effect perceived. The two waves assist each other 
 so nmch the better, as the angle between them is less, and this angle van- 
 ishes in a direction perpendicular to the wind. Hence, in the latter direction 
 the .sound ought to be proj)agatctl a little better than even in the direction 
 of the wind, which agrees with the ex]jerinients of M. Delaroche. Thus, 
 the effect is referred to two known causes, — the increased velocity of the 
 air in ascending, and the ditt'ractioTi of sound. 
 
 As a matter of fact, the phenomenon is much more complicated 
 when one takes into consideration the fact that a wind is ahnost 
 always of very irregular intensities at different altitudes. The 
 phenomenon, in its most complicated form, has been investigated 
 in connection with the subject of fog signals by Professor Osborn 
 Reynolds and Professor Joseph Henry, but with this we are not at 
 l)resent concerned, for the above discussion by Professor Stokes is 
 entirely sufficient for the problem in hand. 
 
 The essence of the above explanation is, therefore, this, that the 
 great difference in loudness of sound with and against the wind is 
 not due to the fact that the sound has been simply carried forward 
 or opposed by the wind, but rather to the fact that its direction has 
 been changed and its wave front distorted. The application of this 
 consideration in the present architectural problem leads to the con- 
 clusion that the greatest benefit will come not from an attempt to 
 carry the sound by the ventilating movement of the air, but by 
 using the motion of the air to incline the wave front forward and 
 thus direct the sound down upon the audience. 
 
 This can be done in either one of two ways, by causing the air 
 to flow through the room from front to back, more strongly at the
 
 EFFECTS OF AIR (T'RREXTS 123 
 
 ceiling than at the floor, or by causing the air to flow from tlie back 
 to the front, more strongly at the floor than at the ceiling. The one 
 process carrying the upper part of the wave forward, the other re- 
 tarding the lower part of I he wave, will tiji the wave in the same 
 way and by an equal amount. 
 
 Again, taking an extreme ca.se, the u.s.Munptioii will be made that 
 the motion of the air is such that it is not moving at or near the floor, 
 that it is moving with its maximum \fl()(it,\- at the ceiling, ami lliat 
 the increase in velocity is gradual from floor to ceiling. Keeping 
 the same amount of air moving as in the preceding calculation, the 
 velocity of the air under this arrangement would be twice a.s great 
 as the average velocity at the ceiling; in tiie preceding case the 
 wave was advanced one centimeter by the motion of the air while 
 traveling the whole length of the hall. In this case, obviously, the 
 upper part of the wave would be carried twice as far, two centime- 
 ters, and the lower part not advanced at all. This would, therefore, 
 measure the total forward tip of the wave. 
 
 Fortunately, the acoustical value of this can be exjiressed in a 
 very simple and practical manner. An inclination of the sound- 
 wave is ecjuivalent acoustically to an eiiual angular inclination of 
 the floor in the opposite direction. The height of the hail being 
 17.9 meters, the inclination forward of the sound-wave would be 
 2 in 1790. The length of the hall being 40 meters, an equal incli- 
 nation, and thus an equal acoustical efl'eet woulil be produced by 
 raising the rear of the floor about 5 centimeters. This considers 
 only the soimd which has come directly from the stage. It is ol>- 
 vious that if the reflection of the sound from the ceiling and the side 
 walls is taken into account, the gain is even less. 
 
 It, therefore, ai)i)ears that, using llie motion of I lie air in the 
 most advantageous wa\' jjossiiile, tlic rouiliiig iniprovemeul in tin- 
 acoustical i)roperty of the hall is of an amount absoluti-ly negligible. 
 A negative result of this sort is jxThaps not so interesting as if a 
 |)ositive advaiitiige has i)een shown; but the problem of proiH-rly 
 heating and ventilating a room is suflieieiilly dillieult in itself, and 
 the above considerations are worth whiK- if only Id free it from this 
 additional coinpliealion.
 
 124 AIU'IHTKCTrHAl> ACOUSTICS 
 
 Temperature 
 
 The offecl of raising tlu- Uinperature of a room, involving as it 
 does the contained air and all the reflecting walls and objects, is 
 twofold. It is not (lidicult to show that, whether we consider the 
 rise in teni])eralurc of I lie air or the rise in temperature of the walls 
 and other reflecting surfaces, the effect of a change of temperature 
 between the limits which an audience can tolerate is negligible, 
 provided the rise in temperature is uniform throughout the room. 
 
 The effect of uniformly raising the temperature of the air is to 
 increase the velocity of propagation of sound in all directions. It 
 is, therefore, essentially unlike the effect produced by motion of 
 the air. In the case of a uniform motion of the air, the sound spreads 
 spherically but with unchanged velocity, moving its center in the 
 direction and with the velocity of the wind. Thus, when blown 
 toward tlie observer, it reaches him as if coming from a nearer 
 source. Blown away from the observer, it arrives as from a more 
 distant source. An increasing temperature of the air increases the 
 velocity, but does not shift the center. The sound reaches the ob- 
 server coming from a source at an unchanged distance. A rise in 
 temperature, therefore, provided it be uniform, neither increases 
 nor decreases the apparent intensity of the sound. The intensity 
 at all points remains wholly unaltered. 
 
 TIic above is on the assumption that the temperature of the air 
 at all points is the same. If the temperature of the air is irregular, 
 the effect of such irregularity may be pronounced; for example, let 
 us assunu' a room in which the temperature of the air at the upper 
 levels is greater than at lower levels. In order to make the case as 
 simple as possible, let us assume that the temperature increases 
 uniformly from the floor to the ceiling. To make the case concrete, 
 let us assume that the hall is the same as that described above, 
 practically rectangular, 40 X 22.8 X 17.9 meters. The velocity of 
 the soimd at the ceiling, the air being uniform, is greater than it is 
 at the floor. In traversing the room the sound-wave will thus be 
 tipped forward. The effect is practically equivalent as before to an 
 increased pitch of the floor or to an increased elevation of the plat- 
 form. Without going into the details of this very obvious calcula-
 
 EFFECTS OF AIR ( lUUEXTS 1^25 
 
 tion, it is sufficient to siiy that in IIr- case of tlie hall here taken as 
 an example, a difference of temperature top and Ijottom of 10° C. 
 would be equivalent to an increase in pitch of the floor sufficient to 
 produce an increased elevation of the very back of 10 centimeters. 
 A difference in temperature of 10° ('. is not excessive, and it is obvi- 
 ous that this has a greater effect than has that of the motion of the 
 air. 
 
 In the above discussion of the effects of motion and of tempera- 
 ture on the acoustical ciuality of a room, it has be(>n assumed that 
 we are dealing solely with the sound which has come directly from 
 the platform. The argument holds to a less degree for the sound 
 reflected from the ceiling and lioni the walls. The above estimates, 
 therefore, are outside estimates. The effect is on the whole cer- 
 tainly less. It is safe to say that the total attainal)le result is not 
 worth the effort that would be involved in altering the architectural 
 features or in comjjromising the engineering ])iaiis. 
 
 But, while uniforui variatinn in liie motion or in the temperature 
 of the air in llie room .ire on the whole negligible factors in its acous- 
 tical character, this is by no nH:in> true of irregularities in the 
 temperature of the air, such as would !»• piniluced iiy a colunin <il 
 warm air rising from a floor inlet. That this is a ])ractical point is 
 shown by the testimony of Dr. David B. Keid beiore the Committee 
 of the Houses of rarliament ])ublislud in its Report of lS;i.5. This 
 conuuittee was appointed to look into the nuitter of the heating, 
 ventilation and acoustics of the lious<s which were being designed 
 to replace those burned in IH'.Vi. Of the gentlemen called before 
 the committee. Dr. Reid gave by far |1h> b(>st testimony, i):irt of 
 which was as follows. 
 
 Speaking of the hall trnipoiMril.N (i((U|)ic(l by I lie House t)f 
 Commons, he s:ii(l: "WiiotluT M>une of inlnruiilion wliirli might 
 be gmirded against is tin- great ImhIv dl' air which 1 prounic arises 
 wheiievt-r the heating ai)i)aralu.s i> in action below. In dillVrenl 
 buildings I have li;id (iceasion to renuirk that whenever lln' alnios- 
 |)here was ])reserved in a >tale (if unity as much a> possible. et|Ual 
 in every respect, the sound was uu)st distinctly audii>le: it occurred 
 to me that when the current of hot air rises from tin- large ap- 
 paratus in the middle of the House of Commons it would very likely
 
 l^e AliCTUTECTURAL ACOT'STICS 
 
 iiilcrftTi' with the conimunication of sound. On inquiry, one of the 
 gentlemen now i)resent lohl nie lie hud frequently observed it was 
 impossible to hear individuals who were on the opposite side of this 
 current, although those at a distance were heard distinctly where 
 the current did not intervene." Elsewhere Dr. Reid said: "A cur- 
 rent of hot air, rising in a broad sheet along the center of the House, 
 reflected the sountl passing from side to side and rendered the in- 
 tonation indistinct. One of the members of the committee, when I 
 exi)lained this circumstance, stated that he had often noticed that 
 he could not hear a member opposite him distinctly at particular 
 times unless he shifted his seat along the bench, and on examining 
 the place referred to, it was found that he had moved to a position 
 where the hot air current no longer passed between him and the 
 member speaking." 
 
 A more recent instance of this sort of difficulty was mentioned 
 to the writer by ^Ir. W. L. B. Jenney, of Chicago, as occurring in 
 his practice, and later was described in detail in a letter from which 
 the following is quoted : 
 
 The hiiildinf; I referred to in my conversation was a court house at 
 IxK-kjiort. No plans exist as far as I am aware. Note the sketch I made 
 from remembrance. 
 
 Note the passage across the room witli stove in center. As the courts 
 were held only during winter there was invariably a fire in that stove. 
 When I examined the room the attendant tliat was with me informed me 
 that the remarks made by the judge, la\\yers and witness could not be 
 heard In' the audience on the opposite side of the passageway containing 
 the stove. 
 
 At that time, the court room not l)eing occupied, there was no fire in 
 the stove and the doors were closed. I experimented; put the attendant 
 in the judge's stand and took position at "A.". I could hear perfectly well. 
 I spoke to liim and he replied, "AMiy, I can hear you perfectly well." I 
 reached tiiis conclusion. Tliat the heated air from the stove and the air 
 supplied by the doors that were constantly fanning at each end of the 
 passageway prodviced a stratum of air of different density from that of 
 the other parts of the room, wliich acted like a curtain hanging between 
 the speakers and the hearers. I made my report verbally to the committee 
 that I left below and brought them with me to the room. The experiments 
 were renewed and they accepted my theory. I recommended that the 
 stove be moved and that the warm air should be let into the room from 
 steam coils below at the the end "A" and taken out by exhaust ventilators
 
 EFFECTS OF AIR ( TTIREXTS 127 
 
 at the end "B." This was done, and I was informed hy the chairman of 
 the comniittee that the result was very satisfactory. Tlie other conditions 
 of the room were quite usual, — plasterinj; on wooden lath, wooden floors, 
 reasonable height of ceiling. 
 
 The above incidents seem to demonstrate fairly clearly thai 
 under certain circumstances abrupt irregularities in temperature 
 may result in marked and, in general, unfavorable acoustical effects. 
 The explanation of these effects in both cases is somewhat a,s follows: 
 
 Whenever sound passes from one medium to another of dili'erent 
 density, or elasticity, a portion of the sound is reflected. The sound 
 which enters the second medium is refracted. The effects observed 
 above were due to these two phenomena, acting jointly. 
 
 The first of the two cases was under simpler conditions, and is, 
 therefore, the easier to discuss. Essentiallj-, it consisted of a large 
 room with speaker and auditor facing each other at a comparatively 
 short distance apart, but with a cylindrical column of hot air rising 
 from a register immediately between. The voice of the speaker, 
 striking this column of air, lost a part by rcfh'clion; a i)art of the 
 sound passed on, entered the coluinii of warm air, and came to the 
 second surface, where a part was again reflected and the remainder 
 went on to the auditor. Thus, the sound in traversing the cohinm 
 of hot air lost by reflection at two surfaces and reached the auditor 
 diminished in intensitj'. It reached the auditor with diminished 
 intensity for another reason. 
 
 The column of warm air acted like a lens. The effect of the 
 column of air was not like that of the ordinary convex lens, 
 which would Ijring the sound to a focus, but rather as a diverging 
 lens. The effect of a convex lens would have been obtained had the 
 column of air been colder than that of the surrounding room. Be- 
 caus«' the air was warmer, and, thcrcl'ori-, tin- velocity of sound 
 through it greater, the eflccl was to cau.se the sound in passing 
 through the cylindrical colulun to diverge even more rapidly and 
 to reach the auditor very coiisiiierably diiiiiiiislicd in iiilcM>ity. 
 AVhich of these two effects was the more jjotcnt in <limiiii>liing the 
 souinl, whether the loss by refltnlion or the loss by Kn>-like (lis|)er- 
 sion was the greater, could only be (leterminc<l if one knew the tem- 
 perature of the air in the room, in I he lolimin. and I he diameter of
 
 1?8 ARCHITECTURAL ACOUSTICS 
 
 tlu' column. It is sufficiont, porliaps, to point out on tlio authority 
 of such cniincnt men as Dr. licid an.l Mr. Jeiniey that the phenome- 
 non is a real one and one to be avoided, and that the explanation is 
 ready at hand and comparatively simple. 
 
 It is, i)erhaps, worlii wiiile pointing out tluit in both of the above 
 cases there was a good deal of reverberation in the room, so that 
 any considerable diminution in the intensity of the sound coming 
 directly from the speaker to the auditor resulted in its being lost 
 in the general reverberation. Had the same conditions as to loca- 
 tion of speaker, auditor, column of warm air and temperature 
 occurred out of doors or in u room of very slight reverberation the 
 effect would have been very much less noticeable. Nevertheless, 
 great irregularity of temperature is to be avoided, as the above 
 testimony fairly clearly shows. 
 
 The above also suggests another line of thought. If, instead of 
 having a single screen of great temperature difference between 
 speaker and auditor, there were many such differences in tempera- 
 ture, though slight in amount, the total effect might be great. This 
 corrt\spon(ls, in the effect produced, to what Tyndall calls a "fioccu- 
 leul eoiulitiou of the atmosphere" in his discussion of the trans- 
 mission of fog signals. Tyndall points out that if the atmosphere 
 is in layers alternately warm and cold sound is transmitted with 
 nnich more rajjid diminution in intensity than when the atmosphere 
 is of very uniform temperature. This phenomenon is, of course, 
 much more important with such temperature differences as occur 
 out of doors than in a room, but it suggests that, in so far as it is a 
 perceptible effect, the temperature of a room should be homogeneous. 
 This condition of homogeneity is best secured by that system of 
 ventilation known as "distributed floor outlets." It has the addi- 
 tional merit of being, perhaps, the most efficient system of ven- 
 tilation.
 
 SENSE OF LOUDNESS' 
 
 It will be showTi here that there is a sense of relative loudness, par- 
 ticularly of equality of loudness, of sounds differing greatly in pitch, 
 that this sense of loudness is accurate, that it is nearly the same for 
 all normal ears, that it is independent of experience, and that, there- 
 fore, it probably has a pliysical and physiological basis. This 
 investigation has been incidental to a larger investigation on the 
 subject of architectural acoustics. It has bearing, however, on 
 many other problems, such, for example, as the standardization of 
 noises, and on the physiological theory of audition. 
 
 The apparatus used consisted of four small organs (Proc. Am. 
 Acad, of Arts and Sciences, 1906)' so widely separated from each 
 other as to be beyond the range of each other's influence. Each 
 organ carried seven night-horn organ pipes at octave intervals in 
 pitch, (>4. 1'28, 256, . . . 4006 vil)rations per second. The four organs 
 were so connected electrically to a small console of seven keys that 
 on pressing one key, any one. any two. any three or all four organ 
 pipes of the same pitch would sound at once, — the comt)inalion of 
 organ pipes sounding being adjusted by an assistant and unknown 
 to the observer. 
 
 In other parts of the investigation on architectural acoustics the 
 loudness of the sound emitted by each of the twenty-eight organ 
 pipes in terms of the niininnim audible sound for the corresi)omling 
 pitch had been determined. The experiment was conducted in the 
 large lecture-room of the Jefferson Physical Laboratory, anil, in 
 I Ik manner ex])lainf(l elsewhere, the computation was made for the 
 loudness of the sound, taking into account the shajie of the roonj 
 and the materials employed in its construction. 
 
 The experiment consisted in adjusting the number of pipes which 
 were souniling or in choosing from among the i)ii)es until such an 
 adjustment was accomplished, that, to an observer in a more or less 
 remote part of the room all seven notes, when souiuled in succession, 
 .seemed to have the same loudness. .\s tlie pi|)es of the same pitch 
 
 ' Contributions from llu- Jc(Trnu)n I'liysical Ijilionitor>'. vol. viii, 1910. 
 » S.f p. 84.
 
 130 SENSE OF L()rDXP:SS 
 
 did not all have the same loudness, it was possible by taking various 
 coinbinafions to make this atljustment with considerable accuracy. 
 Tiiis statement, however, is subject to an amendment in that all 
 four pipes of the lowest pitch were not sufficiently loud anil the 
 faintest of the highest pitch was too loud. 
 
 There were ten observers, and each observer carried out four in- 
 dependent experiments. Speaking broadly, in the case of every 
 observer, the four independent experiments agreed among them- 
 selves with great accuracy. This was to the great surprise of every 
 observer, each before the trial doubting the possibility of such adjust- 
 ment. The results of all ten observers were surprisingly concordant. 
 
 After the experiment with the first two observers, it seemed 
 possible that their very close agreement arose from their familiarity 
 with the piano, and that it might be that they were adjusting the 
 notes to the "balance" of that particidar instrument. The next 
 observer, therefore, was a violinist. Among the observers there was 
 also a 'cellist. Lest the feeling of relative loudness should come 
 from some subconscious feeling of vocal effort, although it is diffi- 
 cult to see how this coidd extend over so great a range as six octaves, 
 singers were tried whose voices were of very different register. Two 
 of the observers, including one of the pianists, were women. Two 
 of the observers were non-musical, one exceedingly so. 
 
 The accompanying table gives the results of the observations, 
 the energy of each sound being expressed in terms of minimum 
 audible intensity for that particular pitch, after making all correc- 
 tions for the reenforcement of the sound by the walls of the room. 
 The observations are recorded in order, the musical characteristic 
 of the observer being indicated. 
 
 Pitch Frequency 
 
 Observers 
 
 
 64 
 
 128 
 
 256 
 
 512 
 
 1024 
 
 2048 
 
 409 
 
 I . Piano 
 
 
 7.0(+)XlC* 1.7X10=4.4X10« 8.0X10«15.0X10« 9.6X10«4.5(- 
 
 i. Piano 
 
 
 7.0+ 
 
 1.7 
 
 4.4 
 
 11.2 
 
 9.2 
 
 12.0 
 
 5.2- 
 
 3. Non-musical 
 
 7.0+ 
 
 1.7 
 
 3.6 
 
 8.9 
 
 6.3 
 
 9.6 
 
 4.5- 
 
 4. Non-mus 
 
 ical 
 
 7.0+ 
 
 1.7 
 
 3.7 
 
 7.7 
 
 14.5 
 
 14.4 
 
 5.6- 
 
 5. Violin 
 
 
 7.0+ 
 
 1.7 
 
 3.5 
 
 11.7 
 
 13.9 
 
 8.0 
 
 3.5- 
 
 6. Violin 
 
 
 7.0+ 
 
 1.7 
 
 4.0 
 
 11.4 
 
 15.5 
 
 15.2 
 
 5.2— 
 
 7. 'Cello 
 
 
 7.0+ 
 
 1.7 
 
 4.2 
 
 12.0 
 
 13.4 
 
 9.6 
 
 5.1- 
 
 8. Tenor 
 
 
 7.0+ 
 
 1.7 
 
 3.9 
 
 13.3 
 
 13.5 
 
 10.5 
 
 4.0- 
 
 9. Soprano 
 
 
 7.0+ 
 
 1.7 
 
 4.7 
 
 12.9 
 
 17.0 
 
 9.6 
 
 5.4— 
 
 10. Piano 
 
 
 7.0+ 
 
 1.7 
 
 3.5 
 
 13.2 
 
 14.5 
 
 8.0 
 
 4.9- 
 
 7.0(+) 1.7 4.0 11.0 13.3 10.6 4.8-
 
 ARCHITFXTURAL ACOUSTICS' 
 
 CORRECTION- OF ACOUSTICAL DIFFICrLTIKS 
 
 v/N the completion of the Fogg Art Museum in 1895, I was re- 
 quested by the Corporation of Harvard Fniversity to investigate 
 the subject of architectural acoustics with the end in view of cor- 
 recting the lecture-room which had been found impracticable and 
 abandoned as unusable. Later the planning of a mw lionie for 
 the Boston Synii)hony Orchestra in Boston widened the scope of 
 the inquiry. Since then, over questions raised first i)y one building 
 and then another, the subject has been under constant investigation. 
 
 In 1900 a series of articles, embody in. i^ llic work of the first five 
 years and dealing with the subject of reverberation, was published 
 in the American Architect and also in the Eiigin<'eriug Becord. The 
 next five years were de\(>t('(l to the extension of this study over the 
 range of the musical scale and the residts were published in the Pro- 
 ceedings of the American Academy of Arts and Scicncfs in 190(i. 
 Since then the investigation lias been with reference to interference 
 and resonance, the effects of peculiarities of form, and the causes 
 of variation in audibility in different i)arts of an auditorium. These 
 result > will be published in anotlu^r article during the ensuing year. 
 
 The i)rogress of this experimental investigation has been guided 
 in practical chaimels and greatly rnriclied by the experience gaiui'd 
 from frequent consultation l)y arcliilecl s, cillicr for purposes of 
 correcting completed buildings or in the prcjjaration of plans in 
 advance of construction. Reserving for a lalt-r article the stimu- 
 lating subject of advance planning, the i)resent article is devoteil 
 to liie problems involved in tiie correction of comi)letcd l)uildings. 
 It is illiistrati'd by a few examples which are especially typical. I 
 desire to lake this ojiportunit}' of expressing my a]>])recialion of 
 IIk' \<ry cordial ])ermission to use this material given by the archi- 
 tects, Messrs. McKini, Mead & AVhite, Messrs. ( 'arrere &: Hastings, 
 Messrs. ("ram, (Goodhue & l-'erguson, and Me»rs. Allen \: Collens 
 
 ' The Architoclurul Quarli-rly uf Ilurvuril l'iiivvr.Hil\ , Munli, iUli. 
 
 »1
 
 13^2 AIUHITErTl'RAL ACOUSTICS 
 
 — to lln'Sf ami to the otlu-r arcliitccts whose confidence in this work 
 has rendered an extensive experience possible. 
 
 The practical execution of this work of correction has recently 
 been placed on a firmer basis by Mr. C. M. Swan, a former graduate 
 stutlent in the T'niversity and an associate in this work, who has 
 taken charge of a dej)artment in the H. W. Johns-]\ranville Com- 
 pany. I am under obligations to him and to this company for some 
 of the illustrations used below, and to the company, not merely for 
 having i)Iaced at my disposal their materials and technical experi- 
 ence, but also for having borne the expense of some recent investi- 
 gations looking toward the development of improved materials, 
 with entire privilege of my making free publication of scientific 
 results. 
 
 It is proposed to discuss here only such corrective methods as 
 can be enii)loyed without extensive alterations in form. It is not 
 proposed to discuss changes of dimension, changes in the position 
 of the wall-surfaces or changes in ceiling height. It is the purpose 
 to discuss here medicinal rather than surgical methods. Such 
 treatment properly planned and executed, while not always avail- 
 able, will in the great majority of cases result in an entire remedy 
 of the difKculty. 
 
 Two old, but now nearly abandoned devices for remedying acous- 
 tical difficulties are stretched wires and sounding-boards. The 
 first is without value, the second is of some value, generally slight, 
 tlioii^li occasionally a perceptible factor in the final result. The 
 stretching of wires is a method which has long been employed, and 
 its disfiguring relics in nuniy churches and court rooms proclaim a 
 diliiculty which they are powerless to relieve. Like many other 
 traditions, it has been abandoned but slowly. The fact that it was 
 wholly without either foundation of reason or defense of argument 
 made it difficult to answer or to meet. The device, devoid on the 
 one hand of scientific foundation, and on the other of successful 
 experience, has taken varied forms in its application. Apparently 
 it is a matter of no moment where the wires are stretched or in what 
 amount. There are theatres and churches in Boston and New 
 York in which four or five wires are stretched across the middle of 
 the room; in other auditoriums miles on miles of wire have been
 
 ACOUSTICAL DIFFICULTIES 
 
 133 
 
 stretched; in both it is equally without effect. In no case can one 
 obtain more than a quahfied approval, and the most earnest nega- 
 tives come where the wires have been used in the largest amount. 
 Occasionally the response to iiupiiries is that "the wires may have 
 done some good but certainly not much," and in general when even 
 that qualified approval is given the installation of the wires was 
 
 F'l(i. I. Ciiliiig of ilmrcli. .Sail Jose, t'iiliforiii:i. showing nn ineffective use of slrelched wires. 
 
 accoiiip;inici| liy some dllicr' cli.iiiui^ of lnrin i>v ipccupiiiicy to which 
 the cretlil should be given. I low extensive an endeavor is .sometimes 
 made in llie use of slrclclicd wires is sliowti by the aeeomi)anying 
 illustration wliicli sli<)W> :i >niail section of I lie ceiling of a church 
 in San Jose, Calil'iinii:!. In llii^ diunli litlwciii mir aini I wo mile-. 
 of wire have lu'cu >lnl(licd with rrsull iug disfigurement, and wholly 
 without avail. Tlic (|Ucslion is being taken up again l>y tlic church 
 for renewed I'il'ort .
 
 I'M ARCHITECTrRAL ACOUSTICS 
 
 Aside from such cuniiiliilivc i-vidfiur of iiu-ttVclivciK-ss, it is not 
 dillicull to show lliat llK-if is no pliysical basis for the device. The 
 sound, whose eclioes these wires are presumed to absorb, scarcely 
 affects the wires, giving to them a vibration wliich at most is of 
 microscopical magnitude. If tlic string of a violin were free from 
 the body of llic violin, if the string of a piano were free from the 
 
 Fio. 2. Congregational Church, Naugatuck, Connecticut. McKim, Mead and White, Architects. 
 
 sounding-board, if the string of a harp did not touch the thin sound- 
 ing-board which faces its slender back, when plucked they would 
 not emit a sound which could be heard four feet away. The sound 
 which comes from each of these instruments is communicated to 
 the air by the vibration of its special sounding-board. The string 
 itself cuts through the air with but the slightest communication of 
 motion. Conversely when the sound is in the room and the string 
 at rest the vibrating air flows past it, to and fro, without disturbing
 
 ACOUSTICAL DIFFICULTIES 
 
 135 
 
 it, and consequently without itself being affected by reaction either 
 for better or worse. 
 
 The sounding-board as a device for correcting acoustical diffi- 
 culties has at times a value; but unless the sounding-hoard is to 
 be a large one, the benefit to l)e exi)ected from its inslallatioii may 
 be greatly overrated. As I his |)articular subject calls for a line dI' 
 
 Kiu. J. Hall of the House of llepresfiitativ<vs, Kliode Isluiul Stale Capilol, rrovidciic-e, K.I. 
 McKim. Mcail ami W'liitc, Arcliitit-ts. 
 
 argument very different from that of tlie main body of the present 
 paper, it will be reserved for a discussion elsewhere, where, s|)aee 
 permitting, it can be illustrated l)y i-xamples of various forms 
 accompanied l)y photographs and by a more or less exhaustive 
 discussion of their relative merits. 
 
 The auditorium in whose special behalf tiiis investigation >tarteil 
 seventeen years ago was tiie lecture-room of the Fogg Art Museum.
 
 13(5 
 
 ARCHirKCTT RAL ACOUSTICS 
 
 Altlu)ii},'li this rouni was in ;i liirj^v iiifasuic rt-iiu'dit'il. it will not be 
 taken as an example. Its jjecnliarities of shape wtic sucli that its 
 complete relief was inherently a complicated process. While this 
 case was chn)nolof,'ically the first, it is thus not suitable for an 
 openinfT illustration. 
 
 .Vnionf,' a numixT ol' iiilcnslinfi; i)roblems in advance of con- 
 si nicl ion the linn ot McKim. ^Fead & White has })ronght .some 
 
 Fk:. i. Dclaii. Hall cf tin- llcnisf oi l{r|)rrsi-Tiliilivcs, Khodc Island State Capitol. 
 M<Kiiii, Mead and While. .Xrehitoets. 
 
 interest inj^- i)roblems in correction, of which three will serve ad- 
 mirably as examples because of llicir unusual directness. The first 
 is that of the Congregational Church in Naugatuck, Connecticut, 
 shown in the accomi)anying illustration. When built its ceiling 
 was cylindrical, as now, but smooth. Its curvature was such as to 
 focus a voice from the platform upon the audience, — not at a point, 
 but along a focal line, for a cylindrical mirror is astigmatic. The 
 
 fl
 
 ACOUSTICAL DIFFICT'LTIES 137 
 
 difficulty was evident with tlic >i)i'iiking, ImiI iiuiy he (lescribed 
 more effectually with reference to the singing. The position of tin- 
 choir was behind the preacher and across the in;iin axis of the 
 church. On one line in tlic andiciicc, crossing tlic cliiiicli ()l)lif|iiely 
 from right to left, the soprano voice couhl be licard coining even 
 more sharply from the ceiling than directly IVotn I lie singer, 'i'he 
 alto starting nearer the axis nl' I Ik- ( IhhcIi IkkI I'or il> locus a hiu- 
 crossing the church less ohliciucly. 'Ilic i)hcnonK'na were similar for 
 the tenor and the bass voices, but with focal lines crossing the 
 church obliquely in opposite directions. The difficulty was in a 
 very large measure remedied by coffering I he ((iling, as shown in 
 the illustration, both the old and the new ceiling being of i)laster. 
 Ideally a larger and fleejier coff<'ring was desiral)l('. l)ut the solution 
 as shown was practical and the result satisfactory . 
 
 The hall of the House of Kcprcscutal ivcs in the Hliodt- Khind 
 State Capitol illu^lralcd aiiollicr l\|ic of dillicully. In cousiilcring 
 this hall it is necessary to bear in uu'nd that the ])r()blcui is an I'ssen- 
 tially different one from thai of a clnii-ch or Iccturc-room. In these 
 the speaking is from a raised i)lalforni and a fixed ])osition. In a 
 legislative assembly I lie -jieakiiig is in I he uiain from I he lloor, and 
 may be from any part of llie floor; Ihe speaker stands on a level 
 with his fellow members; he .stands with his i)ack to a part of the 
 audience, and often with his back to the greater ])art of his audience; 
 in different jyarU of Ihe lion~e the s|)eaker directs his voice in dif- 
 ferent directions, and against different wall-surfaces. In this hall 
 the walls were of stone to ai)i)ro\iiuately half the height of the 
 room; above that Ihey were of stone and plaster. The ceiling was, 
 as shown, coffered. The dillii iilty in this room was with that part 
 of the \-oiee which, crossing Ihe room hansver.sely, fell on Ihe side 
 walls. With the sjjcaker standing on Ihe floor, the greater volume 
 of his voice was directed upward. The -ound striking the side wall 
 
 was reflected across the r i In llie o|i|)osile wall and l)ack again, 
 
 lo and fro. inoiinl iiig gradually until it re.ielnMl the ceiliui,'. It was 
 there retlcetcd direclly douu upon Ihe audience. 'i'he ceiling 
 .slo|)e(l, and had some eur\alure. but llu' curvature was not such 
 as lo produce a distinct focusing of Ihe sound. During Ihoe re- 
 flections Ihe sound mel only feel>ly absorbeiil surfaces ami there- 
 fore returned to the auilielice with but little lo-s of illlen-il>. Us
 
 i:js 
 
 AR(Iiri'E( irRAL ACOUSTICS 
 
 roturn was at such an iiitt-rval of lime as to result in great confusion 
 of speech. ()ni\- thi> fact tliat the voice, rising at different angles, 
 traveled different jjaths and therefore returned at varying inter- 
 vals, i)revented the formation of a distinct echo. The difficulty 
 was remedied in tliis case hy a change in material without change 
 
 Fig. 5. Lecture-room, Metropolitan Museum of Art, New York. 
 MoKim, Mead anil White, .\rchitects. 
 
 of form, bj' diminishing the reflecting power of the two side walls. 
 This was done by placing a suitable felt on the plaster walls between 
 the engaged columns, and covering it with a decorated tapestry. 
 Fortunately, the design of the room admitted of a charming exe- 
 cution of this treatment. It is interesting to note that this treat- 
 ment applied to the lower half of the walls would not have been 
 acousticallv effective.
 
 ACOUSTICAL DIFFICT'LTIES 
 
 139 
 
 The lecture-room of the Metropolitan Museum oi Art illus- 
 trates the next step in complexity. This hall is a semi-circular 
 auditorium, with the semi-circle slightly continued hy short, 
 straight walls. As shown in tlic illustrations the ])latform is nearly, 
 though not wholly, witliin a i)r()ad hut shallow recess. The body 
 
 I'lu. ti. L<.-i turc-roum, Mrlropulilaii MiiM-um cif Arl. Nr« >..rk, 
 Mi-Kiiu. Mtiul uiul Wliitc. Anliil.cls. 
 
 of tlie auditorium is .-.urmounteii l)y a s|)liiTi(;d ceiling witli >liurt 
 cylindrical extension following the straight side walls. In tlie 
 center of the ceiling is a flat skylight of gla.ss. In lliis room the re- 
 verberation was not merely excessive, hut it resolved itself hy focus- 
 ing into a nndti|)le echo, the components of which followed each 
 other with great rapidity hut were distinctly .sepju-ahle. The
 
 140 AlU IIITECTITRAL ACOUSTICS 
 
 nuiiiluT (li.stinguislial)li' variiHl in differiMit parts of tin- hall. Seven 
 were ilislingiiislial)le al cerlain i)arts. A detailed discussion of this 
 is not ajjpropriate in the present paper as it concerns rather the 
 subject of calculation in advance of construction. To improve the 
 acoustics the ceiling was coffered, the limiting depth and dimensions 
 of this cofTeriiig being determined in large measure by the dimen- 
 sions of the skylight. The semi-circular wall at the rear of the 
 auditorium was li-aii.vrornicd inlo panels wliich wi're filled with 
 fell over which was slretclicd huria]) as shown in the second illus- 
 tration. The result was the result assured, — the reduction of the 
 disturbance to a single and highly localized echo. This echo is 
 audible only in the central seats — two or three seats at a time — 
 and moves about as the speaker moves, but in symmetrically opposite 
 direction. Despite this residual effect, and it should be noted that 
 this residual effect was predicted, the result is highly satisfactory to 
 Dr. I'ldward Rot)inson, the Dii'ector of the Museum, and the room is 
 now used with comfort, whereas it had been for a year abandoned. 
 
 It .should be borne in mind that "perfect acoustics" does not 
 mean the total elimination of reverberation, even were that possible. 
 Loudness and reverljcration are almost, though not quite, projjor- 
 tional qualities. The result to be sought is a balance between the 
 two ((ualities, dependent on the size of the auditorium and the use 
 to which it is to be applied. 
 
 Geometrically the foregoing cases are comparatively simple. In 
 each case the room is a simple space bounded by plane, cylindrical 
 or spherical surfaces, and these surfaces simplj^ arranged with refer- 
 ence to each other. The simplicity of these cases is obvious. The 
 complexity of other cases is not always patent, or when jiatent it is 
 not obvious to a luerely casual inspection how best the problem 
 should be attacked. A large number of cases, however, may be 
 handled in a practical manner by regarding them as connecting 
 spaces, each with its own reverberation and pouring sound into and 
 receiving sound from the others. An obvious case of this is the 
 theatre, where the aggregate acoustical propertj' is dependent on 
 the space behind the proscenium arch in which the speaker stands, 
 as well as on the space in front of it. In another sense and to a less 
 degree, the cathedral, with its chancel, transept and nave may be
 
 Fi(i. 7. Di-sign for St. I'lturs Cnllu-ilrnl. D.-lroil. Crnin. (lotxlhuf and Ferguson. .Vrchilocts.
 
 142 ARC IinECTniAL ACOUSTICS 
 
 rt'fiiirded as a caso of conncotcd sj)aC('s. The problem certainly takes 
 on a simpler aspect when so attacked. An extreme and purely hy- 
 pothetical case would he a deep and wide auditorium with a very 
 low ceiling, and with a stage recess deep, high and reverberant, in 
 fact such a cjise as might occur when for special purposes two very 
 <Iifl"erent rooms are thrown together. In such a case the reverbera- 
 tion calculated on the l)asis of a single room of the combined volume 
 and the combined absorbing power would yield an erroneous value. 
 The speaker's voice, especially if he stood back some distance from 
 the oj)eiiing between the two rooms, would be lost in the production 
 of reverberation in its own space. 'J'lie total resulting sound, in a 
 confused mass, would be propagated out over the auditorium. Of 
 course this is an extreme case and of imusual occurrence, but by its 
 very exaggeration serves to illustrate the point. In a less degree 
 it is not of infrequent occurrence. It wjis for this reason, or rather 
 through the experience of this eflfect, although only as a nice refine- 
 ment, that the Boston Symphony Orchestra has its special scenery 
 stage in Carnegie Hall, and for this that Mr. Damrosch in addition 
 moved his orchestra some little distance forward into the main 
 auditorium for his concerts in the New Theatre. 
 
 A cathedral is a good example of such geometrical comijlication. 
 still further complicated by the variety of service which it is to 
 render. It must be adajited to speaking from the pulpit and to 
 reading from the lectern. It must be adapted to organ and vocal 
 nmsic, and occasionally to other forms of service, though generally 
 of so minor importance as to be beyond the range of appropriate 
 consideration. Most cathedrals and modern large churches have 
 a reverberation which is excessive not only for the spoken but also 
 for a large portion of the musical service. The difficulty is not 
 peculiar to any one type of architecture. To take European ex- 
 amples, it occurs in the Classic St. Paul in London, the Romanesque 
 DiU'liani. the Basilican liouianesciue Pisa, the Italian Gothic Flor- 
 ence, and the English (iothic York. 
 
 The most interesting example of this type has been Messrs. Cram, 
 Goodhue & Ferguson's charming cathedral in Detroit, especially 
 interesting because in the process of correcting the acoustics it was 
 possible to carry to completion the decoration of the original design.
 
 Via. 8. St. Paul's Cathedral. Detroit. Cram, Goodhue and Ferguson, .\rchitccts.
 
 U4 AlU'IIITKCTrHAL A( OlSTICS 
 
 rty 
 
 riie nav«-. modt-raloly narrow in the clcroslory. was l)roa(l hi'low 
 throufrli ils i-xtiMision by side aisles. It niiglit fairly be regariled 
 as two simply eonneeted spaces. The lower space, when there was 
 ;i full :Micliciicc. was aluiiiilaiilly al)sorl)cnl ■. Ilu- clcrcslory, Ihoujili 
 with wood ceiling, wius not absorbent. All hough their conil)ine(l 
 reverberation was great, it was not so great as alone to j)roduce the 
 aclnal etlVet obtained. Absorbing material in the form of a felt, 
 highly efficient acoustically, was placcii in the i)atiels on tlie ceiling, 
 'riic i>riginal arcliilcci iiral design by Mr. Cram (Fig. 7) showed the 
 ceiling decorated in colors, and this though not a ])art of the original 
 construction was carried out on the covering of the felt, with a re- 
 sult highly satisfactory both acoustically and architecturally. The 
 transept, also high and reverberant, was similarly treated, as was' 
 also the central tower which was even higher than the rest of the 
 church. As a mailer of fact the results at first attained were satis- 
 factory only with an audience filling at least three-quarters of the 
 seats, the condition lor which it was planned. 'Hie treatment was 
 subsequenll\- extended to the lower levels in order that the cathedral 
 might be serviceable not merely for the normal but for the occa- 
 sionally small audience. The chancel did not need and did not 
 receive any sjiecial treatment. It was highly suitable to the musical 
 service, and being at the back of both the pulpit and the lectern did 
 not greatly affect that portion of the service which called for dis- 
 tinctness of enunciation. 
 
 It may be remarked in j)assing that the lectern is almost invari- 
 ably a more difficult problem than the pulpit. This is in part be- 
 cause reading, with the head thrown slightly forward, is more 
 difficult than speaking; because, if the lectern is sufficiently high 
 to permit of an erect position it screens the voice; because a speaker 
 without book or manuscript, seeing his audience, realizes his dis- 
 tance and his difficulties; and finally, because the pulpit is generally 
 higher and against a column whereas the lectern stands out free and 
 unsupi)orled. 
 
 The auditorium which has received the greatest amount of dis- 
 cussion recently is the New Theatre in New York. Had it been a 
 commercial proposition its acoustical quality would have received 
 but passing notice. As an institution of large purpose on the part
 
 ACOUSTICAL DIFFICT'I/riES 145 
 
 of the Founders il recvived a coriTspoiidiiifrly Iar<;i' atlciilion. As 
 an institvition of generous purpose, without liope or (h'sire for finan- 
 eial return, il was a])propriate(l hy I he jjublie, and received (lie 
 persistent eritieism which seems llie usual reward for >u(li under- 
 takings. The writer was consulted only after the completion of 
 the buildiuf--. hut its acoustical difficulties can he discussed ade- 
 quately only in the light of its inili;d pi'ogranniie. 
 
 It was part of the original i)rogramnie submitted to Messrs. 
 Carrere & Hastings that the building should be used, or at least 
 should be adapted to use for opera as well as for ilrama. In this 
 respect it was to bear to the ISIetropolitan the position which the 
 Opera Comique in Paris bears to the ()j)era. This idea, with its 
 corollary features, influenced the early design .nul ^liows in the 
 completed structure. 
 
 Il was also a part of the initial plan tli.it there >lionid be two 
 rows of boxes, something very unn>ual in thcalrc loiistrnction. 
 'Hiis was a i)ro(ligal use of .space and magnified the Imilding in .ill 
 its ilimensions. Later, but not until after the building was nearly 
 completed, the upper row of bo.xes was abandoned, and the galU-ry 
 thus created was devoted to foyer chairs. As the main walls were 
 by this time erected, tlic gallery wa> limited in depth to the boxes 
 and their antechambers. It thus resulted that this level, which is 
 ordinarily occupied by a gallery of great value, is of small ca))acity. 
 Notwithstanding this the New 'I'heatre seats twenty-three hun- 
 dred, while the usual theatre seats but little more than two-thirds 
 that number. 
 
 The necessity of providing t wenlx-three connnodious boxes, all 
 in the first tier, of which none should be so near the stage as to be 
 distinctly inferior, determined a large circle for their front and ft>r 
 the fi'ont of all the galleries. Thus not nirrcl\- .iic I in- seats, which 
 are orilinarily I lie best, seats, far from tlii' stage, but the great hori- 
 zontal scale thus necessitated leads arehilecturally to a correspond- 
 ingly great vertical scale. I'he row of boxes and the foyer balcony 
 above n<it merely determined the scale of the auditorium, but al>o 
 presenfe<l at the back of their shallow dei)th a concave wall whieii 
 focused file rellectcd .-.ound in the center of the auditorium. 
 
 Finallv, il should be borne in mind Ihat while the acoustical
 
 14(5 AlltlllTECTURAL ACOUSTICS 
 
 clfinauds in :i tlu-iifrc are greater than in almost any oilier lyi)e of 
 auditorium, because of the great modulation of the voice in dra- 
 matic action, the New Theatre was undertaking an even more 
 than usually difficult task, that of presenting on the one hand the 
 older dramas with their less familiar and more difficult phrasing, 
 and on the other the more subtle and delicate of modern plays. 
 
 Kk;. '.>. Intorior, the New Theatre, New York City. Carrere and Hastings, Architects. 
 
 The conventional type of theatre construction is fairly, though 
 only fairly, well adapted to the usual type of dramatic perfornuince. 
 The New Theatre, with a very difficult type of performance to 
 present, was forced by the conditions which surrounded the project 
 to depart from the conventional type far more radically than was 
 perhaps at that time realized. 
 
 Here, as usual in a completed building, structural changes and 
 large changes of form were impossible, and the acoustical difficulties
 
 ACOUSTICAL 1 )I FFICULTIES 
 
 147 
 
 of the auditorium ccjuld \)v renu'died only l)y iiKJiirction. The 
 method 1).\ whicli a very considerable improvement was attained 
 is shown by a comparison of the line drawing (Fig. 10) with the plio- 
 tograpii of the interior of the theatre as originally couiplcted. The 
 boxes were changed from the first to the second Ivvvl, lii'ing inter- 
 changed with the foyer chairs, wliilc I lie excessive height of the 
 main l)o(ly of tlie auditorimn was reduced by means of a canopy 
 surrounding tlic (•culral chandelier. This ingenious and iiol dis- 
 
 Fiu. lU. The New Theatre. New York City, .showing Canopy ami Changed Hoses. 
 
 pleasing substitute for the recommended lowering of the ceiling was 
 proi)o.sed by ^Nfr. Hastings, although of course only as a means to 
 an end. The canopy is oval in plan, following the outline of the 
 oval panel in the ceiling, its longer axis being transverse. Its major 
 and minor liori/.oulal dimensions are 70 f«'et and 40 feet. Its 
 effective lowering of the height of the ceiling is •20 fe<-t. A moment's 
 consideration will show that its effective area in i)reventing the 
 ceiling echo is greater than its acliuil dimensions, particularly in
 
 148 ARCHITECTrHAL ACOUSTICS 
 
 tlu' (iiriK-tion of its minor axis. Tlic iin])rovenient hrouglit al)oul 
 by this was pronouncecl and satisfactory to the Founders. The 
 di.stances, however, were still too great, even visually, for the type 
 of dramatic performance for whicli the theatre was primarily in- 
 tended, and such use was therefore discontinued. The New Tlieatre 
 is nuich better adapted to opera than to dramatic performances, 
 and it will he a matter of great regret if, with its charming solution 
 of many (llllicull arc hilccltiral jjiolilcnis. it is not restored to such 
 dignifietl j)urpose. 
 
 The last and very satisfactory exami)le is lliat of the Chapel of 
 the I'nion Theological Seminary of ^Messrs. Allen & Collens. Its 
 interesting feature is thai the corrective treatment was applied in 
 the process of construction. It is further interesting as an example 
 of a Irealnient which is not merely inconspicuous, hut is entirely 
 intlislinguishable. The pholograpii witlioiit explanation is the best 
 evidence of this (p. 149). 
 
 The above examples have been chosen from many score as typical 
 of the principles involved. In each case the nature of the difficvdty 
 has been stated and the method emi)loyed in its correction, or at 
 least its special feature very brieflj' described. The remainder of 
 I lie i)apcr will he devoted to a discussion of the j)rinciples involved 
 in acoustical correction and in ])resenting the results of some recent 
 exi>eriments. 
 
 Iti discussing the above exam])les, especially the fii'st and the 
 third, tlic Congregational Church in Naugatuck, and the lecture- 
 room oi' the Metropolitan Mu,seiun of Art, consideration had to be 
 given to the effect of the geometrical shape of the room. This 
 aspect of the problem of architectural acoustics constitutes a sub- 
 ject so large that a separate paper must be devoted to its adequate 
 treatment. It involves not merely simple reflection })ut inter- 
 ference and diffraction, as well as the far from simple subject of the 
 pro])agation of soimd jiarallel to or nearly parallel to the jilane of 
 an audience. It has been the object of special investigation during 
 tlic ])ast six years. This investigation has recently come to a suc- 
 cessful issue and will probably be jniblished in full during the en- 
 suing year. It is suitable that it should receive separate pul)lication 
 for, as it concerns shape, it is of more value for calculation in ad-
 
 I'll.. II. ( liiip.j. I iiiiiii riiii.li)«iral Siiiiliiary, Nrw Viirk ( il.\ . Alien iiiul t
 
 1.50 AIU'IIITPXTrRAL ACOUSTICS 
 
 vance of construction than in the correction of conii)Icted buildings. 
 It nnist here suffice to merely indicate the nature of the results. 
 
 When soiuul is produced in a confined auditorium it spreads 
 si)herically from the source until il reaches the audience, the walls, 
 or I lie ceiling. It is there in part absorbed and in part reflected. 
 The part which is reflected ret ra verses the room until it meets 
 another surface. It is again in part absorbed and in i)arl reflected. 
 This process continues until, after a greater or less number of 
 reflections, the sound becomes of negligible intensity. Tluis at aii\- 
 one lime and at any one point in the room there are many sounds 
 crossing each other. In a very simple auditorium, such as a simple 
 rectangular room with plain walls and ceiling, this process is not 
 difficult to follow, eitlier step l)y stej), or In- large, but entirely 
 adequate, generalizations. When the conditions are more compli- 
 cated it is more diflficult to analyze; it is also more liable to be a 
 vitally significant factor in the problem. That it has heretofore 
 been inadequately discussed has arisen from the failure to take into 
 consideration the phenomenon of diffraction in the propagation of 
 a sound nearly parallel to an absorbing audience, the phenomenon 
 of diffraction in reflection from an irregular surface, and. above all, 
 tlie phenomenon of interference. The first of these three considera- 
 tions is of primary importance in calculating the intensity of the 
 sound which has come directly from the source, in calculating the 
 effect of distance in the audience, and in calculating the relative 
 loudness on the floor and in the gallery, and at the front and at the 
 back of the gallery. The second consideration enters into the cal- 
 culation of the path of the sound after reflection from any broken 
 or irregular surfaces. The third is a factor of the utmost impor- 
 tance when the sounds which are crossing at any point in the audi- 
 torium are of comparable intensity and have traveled paths of so 
 nearly equal length that they have originated from the same ele- 
 ment. This latter calls for a more elaborate explanation. 
 
 In both articulate speech and in music the source of sound is 
 rapidly and in general, abruptly changing in pitch, quality, and 
 loudness. In music one pitch is held during the length of a note. 
 In articulate speech the unit or element of constancy is the syllable. 
 Indeed, in speech it is even less than the length of a syllable, for the
 
 ACOUSTICAL DTFFICITI.TIES 151 
 
 open vowel sound wliich forms the Ixjcly of u syllable usually has a 
 consonantal opening and closing. During the constancy of an ele- 
 ment, either of music or of speech, a train of sound-waves spreads 
 spherically from the source, just as a train of circular waves spreads 
 outward from a rocking boat on the surface of still water. Different 
 portions of this train of spherical waves strike different surfaces of 
 the auditorium and are reflected. After such reflection they begin 
 to cross each other's paths. If their paths are so diflferent in length 
 that one train of waves has entirely passed before the other arrives 
 at a particular point, the only phenomenon at that point is pro- 
 longation of the sound. If the space between the two trains of 
 waves be suflBciently great the effect will be that of an echo. If 
 there be a number of such trains of waves thus widely sjjaced, the 
 effect will be that of multiple echoes. On the other hand if the two 
 trains of waves have traveled so nearly equal paths that they over- 
 lap, they will, dependent on tin- difference in length of the paths 
 which they had traveled, either reenforce or mutually destroy each 
 other. Just as two equal trains of water-waves crossing each other 
 may entirelj' neutralize each other if the crest of one and the trough 
 of the other arrive together, so two sounds, coming from the same 
 source in crossing each other may produce silence. This phenom- 
 enon is called interference and is a common phenomenon in all 
 types of wave motion. ()i course this phenomenon has its comple- 
 ment. If the two trains of water-waves so cross that the crest of 
 one coincides with the crest of the other and trough with trough, 
 the effects will be added together. If the two sound-waves be simi- 
 larly retarded, the one on the other, their effects will also be added. 
 If the two trains of waves be equal in intensity, the combined in- 
 tensity will be quadruple that of either of the trains separately, iis 
 above exjjlained, or zero, depending on their relative retardation. 
 The effect of this phenomenon is to produce regions in an audito- 
 rium of loudness and regions of comparative or even comi)lete silence. 
 It is a partial explanation of the so-called deaf regions in an audi- 
 loriuni. 
 
 It is not difficult to observe this phenomenon directly. It is 
 difficult, however, to measure and record the phenomenon in such 
 a nuumer as to permit of an accurate chart of the result. Without
 
 152 ARCHITECTURAL ACOUSTICS 
 
 going into the details of the metliod employed the result of these 
 nieiisurements for a room very similar to the Congregational Church 
 in Naugatuck is sliown in the accompanying chart. The room 
 experimented in was a simple rectangular room with plain side 
 
 Fig. \i. Distribution of intensity on the head level in a room 
 with a barrel-shaped ceiling, with center of curvature on the 
 floor level. 
 
 walls and ends and with a barrel or cylindrical ceiling. The ceiling 
 of the room was smooth like the ceiling of the Naugatuck Church 
 before it was coffered. The result is clearly represented in Fig. 12, 
 in which the intensity of the sound has been indicated by contour 
 lines in the manner employed in the drawing of the Geodetic Survey
 
 ACOUSTICAL DIFFICULTIES 153 
 
 maps. The phenomenon indicated in these diagrams was not 
 ephemeral, but was constant so long as the source of sound con- 
 tinued, and repeated itself with almost perfect accuracy day after 
 day. Nor was the j)]u'nonu>non one wliich could be observed merely 
 instrumenlally. To an observer moving about in the room it was 
 quite as striking a phenomenon as the diagrams suggest. At the 
 points in the room indicated as high maxima of intensity in the 
 diagram the sound was so loud as to be disagreeable, at other i)oints 
 so low as to be scarcely audible. It should be added that this dis- 
 tribution of intensity is with the source of sound at the center of 
 the room. Had the source of sound been at one end and on the axis 
 of the cylindrical ceiling, the distribution of intensity would still 
 have been bilaterally synmietrical, but not symmetrical about the 
 transverse axis. 
 
 As before stated a full discussion of this phase of the subject is 
 reserved for another paper which is now about read}' for publication. 
 
 In the second, in the fourth, and in part in the third of the above 
 examples the acoustical diflTiculty was that of excessive reverberation. 
 
 If a sound of constant pitch is maintained in an auditorium, 
 though only for a very brief time, the sound spreading directly 
 from the source, together with the sounil wliicli has been reflected, 
 arrives at a steady state. The intensity of the sound at any one 
 point in the room is then the resultant of all the superposetl sounds 
 crossing at that point. As just shown, the nuitual interference of 
 these superposed sounds gives a distribution of intensity which 
 shows pronounced maxima and minima. However, the ])r()l)ablc 
 intensity at any point, as well as the aggregate intensity over the 
 room, is the sum of the components. Whatever the distribution of 
 maxima and minima the state is a steady one so long as the source 
 continues to sound. The steady condition in tlic room is mkIi lliat 
 the rate of absorption of the souikI is ((iikiI to llu- rate of emi>>ioii 
 by the source. 
 
 If after this steady state is established I lie source is aliruptly 
 checked, the ditlVreiit trains of waves will continue their jouru<y, 
 the maxima and mininui shifting positions. Ultimately, the .soimd 
 will ceiuse to be audible, having diminished in inleiisily until it has 
 pa.s.sed below what aurisls call the "threshold of audibility." The
 
 154 ARCHITECTURAL ACOUSTICS 
 
 chiralion of iuidihilify after the source hivs ceased is thus dependent 
 upon tlie initial intensity, upon tlie absorbing material, and upon 
 the location of that absorbing material with reference to the several 
 trains of waves. In special cases the position of the absorbing ma- 
 terial is a matter of the utmost importance, but in many cases the 
 aggregate result may be computed on the basis of the total absorbing 
 power in the room. 
 
 The prolongation of the sound in an auditorium after the source 
 has ceased I have ventured to call reverberation, and to measure it 
 mmierically by the duration of audibility after the abrupt cessation 
 of a .source which has producetl an average intensity of sound in the 
 room equal to one million times minimum audible intensity. This 
 is an ordinary condition in actual occurrence. 
 
 In the 1900 papers published in the Engineering Record and the 
 American Architect, this subject of reverberation was discussed at 
 great length, and it was there shown how it might be measured and 
 indeed, how it might be calculated in advance of construction. In 
 addition to the formula many coefficients of absorption were de- 
 termined, such data being absolutely necessary to the reduction of 
 the subject to an exact science. This work related to sounds having 
 a pitch an octave above middle C. 
 
 But it was of course obvious that the acoustical quality of an 
 auditorium is not determined by its character with reference to a 
 single note. The next series of papers, published in 1906, therefore 
 extended the investigation over the whole range of the musical scale 
 giving data for many materials and wall-surfaces, and rendering a 
 more complete calculation possible. At the conclusion of these 
 papers it was shown how the reverberation of an auditorium should 
 be rejjresented by a curve in which the reverberation is plotted 
 against the pitch and by way of illustration a particular case was 
 shown, that of the large lecture-room in the Jefferson Physical 
 Laboratory, both with and without an audience. This curve is 
 reproduced in the accompanying diagram (Fig. 13). 
 
 In the process of investigating an auditorium such a curve 
 should be drawn as definitive of its initial condition and then in the 
 determination of the treatment to be employed similar curves 
 should be drawn representing the various alterations proposed and
 
 ACOUSTICAL DIFFICULTIES 
 
 155 
 
 taking into consideration the location of the surfaces, their areas 
 and the nature of the proposed treatment. The diagram (Fig. 
 14) shows the result of this computation for the more inter- 
 esting of the above examples, St. Paul's Cathedral, Detroit. In 
 this diagram curves are drawn plotting the reverberation of the 
 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^^^1 ~- 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 — o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c. 
 
 c, 
 
 Cj 
 
 c. 
 
 c. c, 
 
 Fig. 13. Curves showing the reverberation in the lecture- 
 room of the Ji'lTrrsoii I'hy.sical l.alMirnlory without an 
 auJienee and witli iin audience lilling all the seat.s. 
 
 ciitlicdral in its original condition, empty, and with a Ihree-ijiiartcrs 
 audience, and with a full audience, and again after its acou>tical 
 correction also empty, witli ;i three-quarters audience, and with a 
 fidl audience. 
 
 Reprints of the pajx-rs just mcnlioned were iiiailed at the time 
 to all members of the American Institute of Architects. l)ui)licales
 
 156 
 
 ARCHITECTURAL ACOUSTICS 
 
 will gladly bo sent to any one who may be interested in the further 
 perusal of the subject. 
 
 Brief mention has l)een made of the dependence, in special cases, 
 of the efficiency of an absorbing material on its positions in an au- 
 ditorium. For example, in the room whose distribution of intensity 
 
 10 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 \ 
 
 \ 
 \ 
 
 \ 
 
 N 
 
 
 ^ 
 y 
 
 X 
 
 X 
 
 v\ 
 
 N 
 
 x* 
 
 y 
 
 
 \ 
 \ 
 \ 
 \ 
 
 \ 
 
 L \ \ 
 
 
 
 
 
 
 \ \ > 
 
 
 
 
 
 
 A \ 
 * \ ^ 
 
 \ 
 
 
 
 
 
 \\ \ \ 
 
 ;-\ 
 
 K 
 
 
 -2--^ 
 
 "^ X 
 
 
 x^ 
 
 
 /: 
 
 / 
 
 -3 -- 
 
 . ^ 
 
 \j 
 
 s;^ 
 
 \3 
 
 / 
 
 ''J 
 -4 
 
 ^ 
 
 
 
 
 
 ^^4- 
 
 
 
 
 
 
 
 
 
 
 O. O, Cj c. c, c. c, 
 
 Fig. 14. Curves showing the reverberation in St. Paul's 
 Cathedral, Detroit, before (1', 2', 3', 4') and after (1, 2, 
 3, 4) corrections, empty and with a one-quarter, one- 
 half, three-quarter and full audience. 
 
 was shown in Fig. 12, the absorbing material would have much 
 greater efficiency in reducing the reverberation if placed so as to 
 include maxima, than if so placed as to include minima. That this 
 would be true is obvious. The magnitude of the effect, however, is 
 not so clear, for the maxima and minima shift as the sound dies
 
 ACOUSTICAL DIFFICULTIES 
 
 157 
 
 away. It was therefore submitted to an accurate experimental 
 investigation. The results are shown in the adjacent diagram. 
 
 
 
 
 
 
 
 / 
 
 \ 
 
 
 
 / 
 
 \ 
 
 
 1.0 
 .9 
 .8 
 .7 
 
 Q 
 
 
 
 / 
 
 \ 
 
 
 
 
 
 
 
 \ 
 
 
 
 j 
 
 
 
 \ 
 
 
 
 1 
 
 2 
 1 
 
 > 
 
 
 \ 
 
 
 
 
 / 
 
 1 
 / 
 
 N 
 
 K^- 
 
 .5 
 4 
 
 
 
 \a 
 
 ( 
 
 
 \ 
 
 
 
 \ 
 
 3 
 \ 
 
 ^ 
 
 V 
 
 3 
 
 
 1 
 
 '// 
 
 
 
 \ 
 
 2 
 
 
 J 
 
 / 
 
 
 
 \ 
 
 1 
 
 ^ 
 
 -y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o, 
 
 c, 
 
 c. 
 
 c> 
 
 c. 
 
 c. 
 
 Kio. 15. .Sliowing lliv ri-liitivc rtjiiu-iuy of fi-ll in tlilliT- 
 eiit parts of a ri>oiii liiiviiiK a harrcl it-iliiiK. Curve 1. 
 uuriiiul al)»orhiiit; ixmcr; ("urvu i. absorliin); jxjwfr in 
 the (TiiliT of tin- room; Curve 3. ulisortiiiiK iM>wrr at 
 the .siilc of I hi- room. Cj i.s miiliilr C, iJU. 
 
 Fig. 15. In tins diagram tlie curve marked 1 >liows hy its vertical 
 
 ordinatcs the iiornial ('(licii'iicy of a very lii^'iiiy aliMirlu-nt felt. If
 
 158 
 
 ARCHITECTTTIAL ACOUSTICS 
 
 so placed in the room as to include on its surface the maxima of 
 intensity of the sound it had an effective absorbing power as shown 
 in Curve 2, a truly remarkable increase over its normal value. 
 Curve 3 shows the effic-iency of the same felt when placed against 
 the side wall. It there included more maxima than minima for the 
 
 1.0 
 
 .9 
 
 .5 
 
 .3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 / 
 
 1 
 
 / 
 
 ""n 
 
 \ 
 
 
 
 
 1- 
 
 N 
 
 \ 
 
 
 
 
 / 
 
 \ 
 
 \\ 
 
 
 
 
 
 
 ^^ 
 
 
 
 
 4 
 
 1 
 
 v^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 c, 
 
 c, 
 
 c< 
 
 c. 
 
 c, 
 
 Fig. 16. Absorbing power of various kinds of felt as de- 
 fined in the text. C3 is middle C, 256. 
 
 lower notes, but more minima than maxima for the higher notes, 
 with a resulting efficiency curve which is very irregidar. 
 
 The following experiments were performed for the H. W. Johns- 
 Manville Company in the search for an efficient absorbing material 
 and an effective method of treatment. The absorbing eflBciency of 
 felt is dependent on the flexibility of the mass as a whole and on its 
 porosity. It is not in large measure dependent on the material
 
 ACOUSTICAL DIFFICULTIES 
 
 159 
 
 employed, except in so far as the nature of that material determines 
 the nature, and therefore the closeness, of the felting process. The 
 same materials, therefore, might very well have either a very high 
 or a very low ahsorljing efficiency, depending entirely upon the 
 process of manufacture. The nature of the material is here specified, 
 
 1.0 
 
 .9 
 
 .8 
 
 .1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,<<^ 
 
 ^ 
 
 
 
 
 I 
 
 f 
 
 \ 
 
 ^ 
 
 
 
 
 i 
 
 
 \ 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 i 
 
 1 
 
 
 
 
 _^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 c, 
 
 c. 
 
 c, 
 
 Fio. 17. Effect of air space behind felt. Curve 1, felt in 
 contact with the wall; Curves 2, 3. and \, felt at dis- 
 tamrs of i. 4, uiid (i inches from the wall. 
 
 not with tlie idea tlial it iilouc can (Iftcnuine tlie (|uality, Kill iniTfly 
 as an additional j)iece of information. In addition to this, in each 
 case the ratio of tlic solid iii.itnial to tlic free .s|)ace is given; l>ul 
 even this does not define in full the essential conditions. The al)- 
 sorbing power is determined not merely hy tiie ratio of the air space 
 to the solid material, but by the size of the pores and by the elns-
 
 lUO 
 
 ARCHITECTLTIAL ACOUSTICS 
 
 ticity and viscosity of the mass as a whole. In Fig. 16 Curve 1 is 
 a hair felt, the one alluded to above as of exceptional efficiency. 
 The fraction of its total volume, which is solid material, is 0.12. 
 Ciu-ve 2 is a mixture of hair felt and asbestos, whose solid portion is 
 
 Fig. 18. Curves showing the effect on absorbing power 
 of membrane covering. Curve 1, felt; Curve 2, burlap 
 cemented with silicate of soda; Curve 3, light mem- 
 brane as described; Curve 4, heavy membrane as de- 
 scribed; lower Curve 3, light membrane alone; lower 
 Curve i, heavy membrane alone. 
 
 0.19 of its total volume. Curve 3 is a felt wholly of asbestos f" 
 thickness, whose solid portion is 0.33 of its total volume. In this 
 latter the asbestos fiber is felted to an asbestos cloth which serves 
 to strengthen it greatly. Curve 4 is for an asbestos felt without 
 reenforcement. That a considerable fraction of its absorbing power
 
 ACOUSTICAL DIFFICULTIES Kil 
 
 is tliie to its elastic yii-lding jis a whole is shown by its rather sharp 
 maxima. 
 
 The curves in Fig. 17 show the effect of holding the felt at differ- 
 ent distances from the wall. In each case it was held on a wire 
 grating. Curve 1 is when the felt is as near the wall as the grating 
 would permit, perhai)s within a quarter of an inch of the wall. 
 Curve 2 is when the IVll was held at a distance of two inches; Curve 
 ;5 at four inches; and Curve 4 at sL\ inches from the wall. It is 
 evident that there is a slight gain from an air space behind the felt, 
 but it is alkO evident that this gain is so shght as to be entirely 
 incommensurate with the cost of construction and its loss in dur- 
 ability. 
 
 The Curves in Fig. 18 show the efficiency of various coverings. 
 Curve 1 is the normal exjjosed efficiency of the felt above referred 
 to. Curve 2 is its efficiency when covered by burlap attached by 
 silicate of soda. This covering was so sized as to be practically 
 impervious, but was in contact with and a part of the felt. Curves 3 
 and 4 show the efficiency of coverings which are not in contact with 
 the felt, but wliicli are .stretched. Both coverings are impervious, — 
 3 relatively light, 4 heavy. Number 3 weighs 0.87 ounces to the 
 square foot; number 4 weighs 2.58 ounces to the square foot. The 
 materials of which these coverings are made have no bearing on the 
 question, and would be misleading if stated. The really significant 
 factors are their weight, the tension with which they are stretched, 
 their elasticity, and their viscosity. The weight of the several 
 coverings hjis been stated; the other factors can be defined best by 
 means of their independent absorbing j)owers. Lower curves 3 and 4 
 indicate the ab.sorbing |)()wcr of the niemljrane coverings alone. 
 It is interesting to note that the diaphragm which has by itself the 
 least absorbing power has tlic grcat.^l absorbing jwwer when 
 combined with th(> fell. This is l)y no means a i)aradox. H is 
 exactly the result which could l)e i)redieted by application of the 
 simplest of physical princijjles.
 
 THEATRE ACOUSTICS' 
 
 ViTRUVirs, De Architectura, Liher V, Cap. VIII. (De locis con- 
 sonantibus ad theatra eligendis.) 
 
 " All this being arranged, we must see with even greater care that a 
 position has been taken where the voice falls softly and is not so reflected 
 as to produce a confused effect on the ear. There are some positions offer- 
 ing natural obstructions to the projection of the voice, as for instance the 
 dissonant, which in Greek are termed n.aTr]xolvTK\ the circumsonant, which 
 with them are named TrepiTjxoiVres ; and again the resonant, which are termed 
 avTTi]XO^''Ti%. The consonant positions are called by them o-iTijxoicTes. 
 
 The dissonant are those places in which the sound first uttered is carried 
 up, strikes against solid bodies above, and, reflected, checks as it falls the 
 rise of the succeeding sound. 
 
 The circumsonant are those in which the voice spreading in all direc- 
 tions is reflected into the middle, where it dissolves, confusing the case 
 endings, and dies away in sounds of indistinct meaning. 
 
 The resonant are those in wliidi the voice comes in contact with some 
 solid substance and is reflected, producing an echo and making the case 
 terminations double. 
 
 The consonant are those in which the voice is supported and strength- 
 ened, and reaches the ear in words which are clear and distinct." 
 
 This is an admirable analysis of the problem of theatre acoustics. 
 But to adapt it to modern nomenclature, we must substitute for the 
 word dissonance, inlerforence; for the word circunisonance. rever- 
 beration; for the word resonance, echo. For consonance, we liave 
 unfortunately no single term, but the conception is one which is fun- 
 damental. 
 
 It is po.ssible that in the above translation and in the following 
 interpretation I iiave read into the text of Vitruvius a dcfinitcness of 
 concei)tion and an accord with modern science which his language 
 only fortuitously permits. If so, it is erring on the better side, and is 
 but a reasonable latitude to take under the circumstances. The only 
 passage whose interpretation is open to serious (lucstion is that rc- 
 
 ' Tlif .ViniTirati Anliitwt, viil. rlv. p. ii'i. 
 las
 
 I(i4 THEATRE ACOUSTICS 
 
 latinj; to dissonant i)laces. If Vitruvius knew that the superposition 
 of two sounds could produce silence, and the expression "opprimit 
 inseqiientis vocis elationem" permits of such interpretation, it must 
 stand as an observation isolated by many centuries from the modern 
 knowledge of the now familiar phenomenon of interference. 
 
 Interferenxe 
 
 Interference is a phenomenon common to all types of wave motion. 
 The best introduction to its discussion is by reference to water-waves 
 
 Fio. 2. Greek Theatre at the University of California. Mr. John Galen Howard, Architect. 
 
 and in particular to an interesting example of tidal interference on 
 the Tongking Peninsula. The tide of the Pacific Ocean enters the 
 Chinese Sea through two channels, one to the north of the Philippine 
 Islands, between Luzon and Formosa, and the other through the 
 Sulu Archipelago between Mindanao and Borneo. The northern 
 channel is short and deep; and the tide enters with very little re- 
 tardation. The other channel, although broad, is shallow, tortuous, 
 and broken by many small islands ; and the tide in passing through 
 is nuicli retarded. The two tides thus entering the Chinese Sea pro- 
 duce an effect which varies from point to point. At one port on the 
 Tongking Peninsula, these tides are so retarded relatively to each 
 other as to be six hours apart. It is high tide by one when it is low 
 tide by the other. It also so happens that at this point the two tides
 
 THEATRE ACOUSTICS 165 
 
 are equal. Being equal and exactly opposite in phase, they neutralize 
 each other. 
 
 Because tidal waves are long in comparison with the bodies of 
 water in which they are propagated, their interference phenomena 
 are obscure except to careful analysis, ^^^len, liowever. the waves 
 are smaller than the space in which they are being propagated, the 
 interference system becomes more marked, more complicated, and 
 more interesting. Under such circumstances, there may be regions 
 of perfect quiet near regions of violent disturbance. 
 
 Subjecting the parallel to a more exact statement, whenever two 
 water-waves come together the resulting disturbance at any instant 
 is equal to the algebraic sum of the disturbances which each would 
 produce separately. If their crests coincide, the joint effect is equal 
 to the sum of their sei)arate effect. If crest and trough coincide, their 
 joint effect is the ditference between them. If their relative retarda- 
 tion is intermediate, a wave results which is intermediate between 
 their sum and their difference and whose time of maximum does not 
 occur simultaneously with the niaxinuim of either of the components. 
 
 The i)lienomenon is one which may be produced accurately on 
 any scale and with any type of wave motion. Thus sound consists 
 of waves of alternate condensation and rarefaction in the air. If two 
 trains of .sound-waves cross each other so that at a given point con- 
 densation in the two trains arrive simultaneously, the rarefactions 
 will al.so arrive simultaneously, and the total dislurl)ance is a train 
 of waves of condensation and rarefaction equal to the sum of the two 
 components. If one train is retarded so that its condensations coin- 
 cide with the ()ther's rarefactions, llie disturbance produced is the 
 difference between that whicii would be produced by the trains of 
 waves separately. Just as a tidal wave, a storm wave, or a ri[)i)le 
 may be made to separat<' and recross by some obstacle nnuul \\ lii( h 
 it diffracts or from whicii it is reflected, and reeoinbining proiluee 
 regions of violent and regions of mininuun disturbances, so sound- 
 waves may be diffracted or reflected, and recomi)ining after travel- 
 ling different paths, produce regions of great loudness aiul regions of 
 almost complete silence. In general, in an auditorium the phenom- 
 enon of interference is produced not l)y the crossing of two trains of 
 waves only, but by the crossing of many, reileeted from the various
 
 IGG THEATRE ACOUSTICS 
 
 walls, from the ceiling, from the floor, from any obstacle whatever 
 in the room, while still other trains of waves are produced by the 
 diffraction of the sound around columns and pilasters. 
 
 A source of sound on whose steadiness one can rely is all that is 
 necessary in order to make the phenomenon of interference obviovis. 
 A low note on a pure toned stop of a church organ will serve the 
 purpose admiral)ly. The observer can satisfy himself that the note 
 is sounding steadily by remaining in a fixed position. As soon, how- 
 ever, as he begins to move from this position by walking up and down 
 the aisle he will observe a great change in loudness. Indeed, he may 
 find a position for one ear which, if he closes the other, will give al- 
 most absolute silence, and this not far from positions where the 
 sound is loud to the extent of being disagreeable. The observer in 
 walking about the church will find that the phenomenon is compli- 
 cated. It is, however, by no means random in its character, but 
 definite, pennanent, and accurate in its recurrence, note for note. 
 Tlie phenomenon, while difficult, is by no means impossible of experi- 
 mental investigation or of theoretical solution. Indeed, this has been 
 done with great care in connection with the study of another prob- 
 lem, — that of the Central Criminal Court Room in London known as 
 Old Bailey. The full primary explanation of the methods and results 
 of this general investigation would be inappropriately long in an 
 article dealing with the acoustics of theatres; for while interference 
 is a factor in every auditorium, it is on the whole not the most 
 seriously disturbing factor in theatre design. 
 
 The subject of interference would not have been given even so 
 extended a discussion as this in a paper dealing with theatres were 
 it not that recently there has been proposed in Germany a fonn of 
 stage setting known as the Kuppel-horizont for sky and horizon 
 effects, to accompany the Fortuny system of stage lighting, in which 
 interference may be a not inconsiderable factor unless guarded 
 against. The Fortuny system, which in the opinion of some com- 
 petent judges is an effective fonn of stage lighting, consists primarily 
 in the use of indirect illumination, softened and colored by reflection 
 from screens of silk. As an adjunct to the system, and in an en- 
 deavor to secure a considerable depth to the stage without either 
 great height or an excessive use of sky and wing flies, a cupola is
 
 THEATRE ACOUSTICS 
 
 167 
 
 recommended to go with the Fortuny lighting as shown in the ac- 
 companying figures taken from the pubHcations of the Berliner Alle- 
 gemeine Electriciiats Gesellschuft. In Figs. 3 and 4, the cupohi is 
 shown in section and in i)l:iii. Liglits A and B illuminate the interior 
 of the cupola; C and K light the area of the stage on which the prin- 
 
 CU^TAiN DRaPCR t 
 
 OKCMtSTlA ? r 
 
 
 PLAN 
 
 Figs. 3 and 4. Sorlion niul plan of tlir Kiippel-Horijx)!!! 
 with Fortuny systriii of liKliliiiR. 
 
 cipal action occurs. Cloud (fTccts, either stationary or moving, are 
 ])rojected on the surface of the cupola i)y a stereoi)ticon. The great 
 advantage claimed for this form of stage setting is the more natural 
 arrangement of stage properties wliidi it makes possible, and the 
 elimination of numerous (lies. On tiie other hand there is .sonu' criti- 
 cism that this lighting results in an unnatural silhouetting.
 
 1(>8 
 
 THEATRE ACOUSTICS 
 
 So (K-taiIrd an exi)lanatioii of the diagrams and the purpose of the 
 several parts is necessitated by the fact that it is as yet an unfamiHar 
 device in this country. It has been introduced recently in a number 
 of theatres in Germany, although I believe not elsewhere, unless 
 possibly in one theatre in England. It has been called to my atten- 
 tion by Professor Baker as a possible equipment of the theatre which 
 
 Fig. 5. Interference system for tennr C in the Kuppel-Horizont, 
 having a tliirty-six foot proscenium opening. The intensity 
 of sound is represented by contour lines, the maximum vari- 
 ation being forty-seven fold. 
 
 is proposed for the dramatic department of Harvard University, and 
 it is reasonable to regard it as a probable factor in theatre design in 
 other countries than Germany. 
 
 In Fig. 5 is plotted the interference system established in this 
 space, on a standing head level of five feet from the floor of the stage, 
 by a sustained note tenor C in pitch. The intensity of the sound is 
 indicated by contour lines very much as land elevation is indicated 
 on the maps of the Geodetic Survey. In this plot, account has been 
 taken of the sound reflected from the cupola and from the floor. No 
 account has been taken of the reflection from the walls of the main 
 auditorium since this would be a factor only for sounds prolonged 
 beyond the length of any single element in articulate speech. Even 
 in the case of a very prolonged sound the modification of the inter-
 
 THEATRE ACOUSTICS l(i!) 
 
 ference system of the stage and cupola by the rest of the auditorium 
 would be very slight. 
 
 The interference system on the stage in question being deter- 
 mined wholly by the floor and cupola, it may be computed, and in 
 the preparation of tlie chart was computed, by the so-called method 
 of images. The sound reflected from the floor comes as from a virtual 
 image as far beneath the floor as the mouth of the speaker is above 
 it. Each of these produce real images by reflection from the interior 
 of the cupola. Bearing in mind that these real inuiges show the 
 phenomenon of diffraction and some astigmatism, and taking into 
 account the phase of the sound as determined by reflection and by 
 distance, the calculation is laborious but not difficult. It involves 
 but the most familiar processes of geometrical optics. 
 
 The disturbing effect of this interference system is not so great 
 when the speaker is well in front of the center of curvature of the 
 cupola, and of course it is almost always more or less broken by the 
 stage properties, as indicated in Figs. :5 and 4. Nevertheless, it is 
 well to bear in mind that the (piarler s])liere form, as indicated in the 
 diagrams, is neither neces.sary from the standpoint of illumination 
 nor desirable from the standpoint of acoustics. Acoustically a flatter 
 back with sharper curvature above and at the sides is preferable. 
 
 It shovdd be repeated that the interference .system is established 
 only when the tones are sustained, in this case over one-tenth of a 
 second, and is more of an annoyance to the actor on the stage than 
 to the audience. With shorter tones it becomes an echo, and in this 
 form is quite as annoying to the audience as to the actor. It should 
 be added that the interference changes with change of pitch, but 
 preserves extreme maxima and minima for a central jjosition in a 
 spherical or partly spherical surface. Finally in music, since sus- 
 tained tones occur more than in si)eech. the interference is more dis- 
 turbing. The efl'ecl of >uch >])lierical stage recesses on nnisic is 
 shown i>y those otiicrwisc inmsually cxcflhiit auditorimiis. Orches- 
 tra Hall in Chicago, and llie Concert Hall at Willow (Irovc Park 
 near I'hiladelphia.
 
 170 THEATRE ACOUSTICS 
 
 Re\'erberation" 
 
 " Circumsonant places" were rare and almost wliolly negligible 
 difficulties in Greek and Roman theatres. However, they were com- 
 mon in tlie temples, and were even more pronounced in some of the 
 older Roman palaces. It must have been in the experience of such 
 conditions, wholly foreign to the theatre of which he was writing, 
 that Vitruvius made this portion of his analysis of the acoustical 
 l)roblem. Given the fundamental form of the Greek theatre, it re- 
 quired no special consideration and little or no skill to avoid such 
 (lifrKulties. However, this is not true of the modern theatre, in which 
 excessive reverberation is more often the defect than any other 
 factor. 
 
 If a sound be produced briefly in a wholly empty, wholly closed 
 room, having perfectly rigid walls, it will be reflected at each inci- 
 dence with undiminished intensity, and, travelling to and fro across 
 the room, will continue audible almost indefinitely. Of course no 
 theatre, ancient or modern, satisfies these conditions and the sound 
 loses at each reflection, diminishing in intensity, until in the course of 
 time it crosses what the experimental psychologist calls the "thresh- 
 old of audibility." In the Greek theatres the duration of audibility 
 of the residual sound after the cessation of a source of ordinary loud- 
 ness was never more than a few tenths of a second; in a modern 
 theatre it may be several seconds. The rapidity with which the 
 sound dies away depends on the size of the theatre, on its shape, on 
 the materials used for its walls, ceiling, and furnishings, and on the 
 size and distribution of the audience. The size and shape of the 
 theatre determines the distance travelled by the sound between 
 reflections, while the materials determine the loss at each reflec- 
 tion. No actual wall can be perfectly rigid. Wood sheathing, 
 plaster on wood lath, plaster on wire lath, plaster applied directly 
 to the solid wall, yield under the vibrating pressure of sound and 
 dissijKite its energy. Even a wall of solid marble yields slightly, 
 transmitting the energy to external space or absorbing it by its own 
 internal viscosity. 
 
 Absorptions by the walls and other objects in the process of reflec- 
 tion, including in this transmission through all openings into outer
 
 THEATRE ACOUSTICS 171 
 
 space as ec|uivalcnt to total ahsoq^tion — boundary conditions in 
 other words — are ])racti('aliy alone (o he credited with the dissolu- 
 tion of tiie residual sound. I5ul \ilruvius' statement that the 
 sound "is reflected into the luiddie. where it dissolves" challenges 
 completeness and at least tiie mention of another factor, which, 
 because of its almost infinitesimal inii)ortance, woidd otherwise be 
 passed without connnent. 
 
 Assimiing, what is of course impossible, a closed room of ab- 
 solutely rigid and perfectly reflecting walls, a sound once started 
 would not continue forever, for where the air is condensed by the 
 passing of the wave of sound, it is heated, and where it is rarefied, it 
 is cooled. Between these uiUMiually heated regions and between 
 them and the walls, there is a continual radiation of heat, with a re- 
 sulting dissipation of available energy. In the course of time, but 
 only in the course of a very long time, the sound would even thus 
 cease to be of audible intensity. This form of dissijnition might well 
 be called in the language of Vitruvius "solvens in medio": but. in- 
 stead of being an important faddi-, il is an entirely negligible factor 
 in any actual auditorium. 
 
 Practically the rapidit\' with whicii tin' sound is absorlied is de- 
 pendent solely on the nature of the reflecting surfaces and the length 
 of the path which the sound nuist traverse between reflections, the 
 latter depending on the shajjc and si/e of the auditorium. It was 
 shown in a series of papers i)ut)lished in The American Architect in 
 1900,' and in another paper published in the Proceedings of the Amer- 
 ican Academy of Arts and Sciences in 1906,' that, given the jilan^ of 
 an auditorium and the material of which it is composetl, it is ])ossible 
 to calculate with a very high degree of accm'acy the rate of decay of 
 a sound in the room and the duration of its audibility. In the first of 
 the above papers there was given the comi)l(tc theory of llie subject, 
 together with tables of experimentally determinetl coelHcients of ab- 
 sori)tion of sound for practically all the materials that enter into 
 auilitorium construction, for sounds lia\ing a ])ileh one octave aliove 
 middle C (vibration fr<'(|uene_\ .Jl'2). In the second of tlie alici\e 
 papers llicre were gi\cn the eoeilieients of ab'-oiption of liuilding 
 material-- foi- tli<' wholr laiige of the nuisical scale. 
 
 ' >i' piiKr (l!i. • Iliiil.
 
 M^i 
 
 THEATRE ACOUSTICS 
 
 In the careful design of a room for musical jjurjioses, the problem 
 obviously must include the whole range of the musical scale, at least 
 seven octaves. It is not so obvious that the study must cover so 
 great a range when the primary use is to be with the spoken voice. 
 The nearest study to architectural acoustics is the highly develojjed 
 science of telephony, and in this it is a])parently sufficient for much 
 of the work to adapt the theory and design to the single frequency of 
 800, api)roximately A in the second octave above middle C. But for 
 
 Fig. 6. The Little Theatre, New York. Ingalls and Hoffman, Architects. 
 
 some problems the in\'estigatioii must be extended over a consider- 
 able range of pitch. Similarly experience in the architectural prob- 
 lem shows that with some of the materials entering into building con- 
 struction there occurs a sharp resonance within a not great range of 
 pitch. It is, therefore, necessary to determine the reverberation even 
 for the speaking voice, not for a single pitch but for a considerable 
 range, and the quality of a theatre with respect to reverberation will 
 be represented by a curve in which the reverberation is plotted 
 against the pitch. 
 
 Without undertaking to give again a complete discussion of the 
 theorj' of reverberation, and referring the reader to the earlier (1900) 
 numbers of The American Architect, it will suffice to give a single
 
 rnaao-QDDQmD 
 
 ti^ 
 
 3C3 
 
 
 TT-r; 
 
 Fl09. 7 an<i 8. Plan ami Sct-liim of tin- LillK- Tlifulir. NVw York. 
 IiiftalU uikI IhitTinuii. Aixliititls.
 
 174 THEATRE ACOUSTICS 
 
 illustration. For this I have selected Mr. Wintlirop Ames' "Little 
 'J'heatre" in New York, designed by Messrs. Ingalls and Hoffman, 
 because the purpose and use of this auditorium was defined from the 
 beginning with unusual precision. The purpose was the production 
 of plays which could be adequately rendered only by the most deli- 
 cate shades of expression, which would be lost in considerable meas- 
 ure if the conditions were such as to necessitate exaggeration of 
 feature or of voice. The definition of its use was that it should seat 
 just less than 300, and that all the seats were to be as nearly as 
 possible of equal excellence, with the important assurance that every 
 seat would be occupied at every performance. 
 
 The final plan and section of the Little Theatre are shown in 
 Figs. 7 and 8. The initial pencil sketch was of an auditorium differ- 
 ing in many architectural details, acoustical considerations sharing 
 in, but by no means alone dictating, the steps leading to the final 
 solution of the problem. The first calculations, based on the general 
 lines of the initial sketch, and assuming probable materials and plaus- 
 ible details of construction (plaster on tile walls, plaster on wire lath 
 ceiling, solid plaster cornices and moulding), gave a reverberation as 
 shown in Curve 1 in Fig. 9. This would not have been in excess of 
 that in many theatres whose acoustical qualities are not especially 
 questioned. But the luiusual requirements of the plays to be pre- 
 sented in this theatre, and the tendency of the public to criticize 
 whatever is unconventional in design, led both ]\Ir. Ames and the 
 architects to insist on exceptional quality. The floor was, therefore, 
 lowered at the front, the ceiling was lowered, and the walls near the 
 stage brought in and reduced in curvature, with, of course, corre- 
 sponding changes in the architectural treatment. The rear wall, 
 following the line of the rear seats, remained unchanged in curvature. 
 The side walls near the stage were curved. The net effect of these 
 changes was to give an auditorium 28 feet high in front, 23 feet high 
 at the rear, 48 feet long and 49 feet broad, with a stage opening 18 
 by 31, and having a reverberation as shown by Curve 2. In order to 
 reduce still further the reverberation, as well as to break acoustically 
 the curvature of the side and rear walls, "acoustic felt" was applied 
 in panels. There were three panels, 6 feet by 13 feet, on each of the 
 side walls, and seven panels, two 4 feet 5 inches by 13 feet, two 5
 
 THEATRK A( OT'STICS 
 
 r 
 
 feet by 10 feet, two 2 feet hy 4 iVil, and one 8 feet by 7 feet, on the 
 rear wall. The resulting reverberation is shown bj Curve 3 in the 
 diafjrain. Throughout, consideration was had for the actual path of 
 the sound in its successive reflections, but the discussion of tliis 
 
 8 
 
 8 
 7 
 6 
 5 
 4 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1^ 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 \ \ ^ 
 
 v^--^ 
 
 .^ 
 
 ] 
 
 
 
 2 
 
 
 
 
 
 
 \. 
 
 
 
 
 1 
 
 ' 2 
 
 ~3 
 
 ^- 
 
 -^ 
 
 
 
 
 
 
 
 o, 
 
 c, 
 
 c. 
 
 c, 
 
 c. 
 
 c, 
 
 Kio. !>. Hovfrlirriilioii in sounds of llie Liltlr Tlicatrr. 
 for iioU-s of (liirtTi-iil |)il<li.('] Iwiiif; MiililleC, Curve I 
 f(ir llir lirst <l<slt;M, Curve i for the seoiml.nnil Curve 
 ;l for llie tliiril and as liulll. 
 
 jiliasi' of (lie gi-neial i)i()l)lcni conu-.s in llie next sctlion and will be 
 illustrated by otlier tluatres. 
 
 It should be said. ])jiniiliirli(ally Iml none llic less cMiplialieally, 
 that throughout this iKipcr l>y Iheatif i> nuaiit an auditorium for 
 tli('s])ok('n dranni.
 
 17(i THEATRE ACOUSTICS 
 
 Echo 
 
 When a source of sound is maintained constant for a sufficiently 
 \ouii time — a few seconds will ordinarily suffice — the sound be- 
 comes steady at every point in the room. The distribution of the 
 intensity of sound under these conditions is called the interference 
 
 Vie. l(t. Interior, the New Theatre, New York. Carrere and Hastings, Architects. 
 
 system, for that particular note, of the room or space in question. 
 If the source of sound is suddenly stopped, it requires some time for 
 the sovuid in the room to be absorbed. This prolongation of sound 
 after the source has ceased is called reverberation. If the source of 
 sound, instead of being maintained, is short and sharp, it travels as 
 a discrete wave or group of waves about the room, reflected from 
 wall to wall, producing echoes. In the Greek theatre there was ordi-
 
 THEATRE ACOUSTICS 
 
 r 
 
 narily hul one echo, "doubling the case ending," while in the modern 
 theatre there are many, generally arriving at a less interval of time 
 after the direct sound and therefore less distinguishable, but stronger 
 and therefore more disturbing. 
 
 This pliase of the acoustical jiroblem will be illustrated by two 
 examples, the New Theatre, the most important structure of the 
 
 Vw.. II 
 
 kind in New York, and the plans of the theatre now building for the 
 Scollay Square Realty Company in Boston. 
 
 Notwithstanding the fad that there was at one time criticism of 
 the acoustical (|uaiity of the New 'J'heatre, the memory of which 
 still lingers and slill colors the casual coininent, it was not worse in 
 proportion to its size than several ollur theatres in the city. It is, 
 therefore, not taken as an example because it showed acoustical de- 
 fects in reniarkal)if degree. l)nl rather Ix-canse there is much that 
 can be learned from the conditions under whidi it was i)uill, i>ecau.se 
 such defects as existed have been corrected in large measure, and
 
 178 
 
 THEATRE ACOI STICS 
 
 above all in the liojie of aiding in some small way in the restoration 
 of a magnificent l)uiUling to a dignified use for which it is in so many 
 ways eminently suited. The generous purpose of its Founders, the 
 high ideals of its manager in regard to the plays to be produced, and 
 the jierfection otherwise of the building directed an exaggerated and 
 morbid attention to this feature. Aside from the close scrutiny which 
 
 Fig. 12 
 
 always centers on a semi-public undertaking, the architects, Messrs. 
 Carrere and Hastings, suffered from that which probably every archi- 
 tect can appreciate from some similar experience of his own, — an 
 impossible program. They were called on to make a large "little 
 theatre," as a particular type of institution is called in England; and, 
 through a division of purpose on the part of the Founders and Ad- 
 visers, for the Director of the Metropolitan Opera was a powerful 
 factor, they were called on to make a building adapted to both the 
 opera and the drama. There were also financial difficulties, although 
 very different from those usually encountered, a plethora of riches. 
 This necessitated the provision of two rows of boxes, forty-eight 
 originally, equally commodious, and none so near the stage as to
 
 THEATRE ACOUSTICS 
 
 179 
 
 thereby suffer in coniparisoii with the others. Finally, there was a 
 change of program when the building was almost complete. The 
 upper row of boxes was abandoned and the shallow balcony thus 
 created was devoted to Unrr chairs wliich were reserved for the 
 
 ■TW NlwmtATlt 
 
 Ki(i. l.'i. I'laiis aiul Section of llu- Now Tlioalre, New York. 
 Carr^re and Mostings, Architects. 
 
 annual subscribers. As will l>c sIkiwu later these .seats were acousti- 
 cally the i)oorest in the !inu>e. 
 
 Encircling boxes are a familiar arrangement, but most of the 
 precedents, especially those in good repute, are oi)era houses and 
 not theatres, the oj)era and tiie drama being ilitVcrent in tlieir acous- 
 tical requirenunts. In the New Theatre this arrangement exertetl a 
 three-fold pressure on the design. It raised the l)aleony and gallery ^^2 
 feet. It increased both the breadth and tluMlei)th of the house. And. 
 together with the re(|uirement that the.se boxes shoidd not extend
 
 180 THEATRE ACOUSTICS 
 
 near the stage, it led to side walls whose most uatiual architectural 
 treatment was such as to create sources of not inconsiderable echo. 
 The immediate problem is the discussion of the reflections from 
 the ceiling, from the side walls near the stage, from the screen and 
 parapet in front of the first row of boxes and from the wall at the 
 rear of these boxes. To illustrate this I have taken photographs of 
 the actual sound and its echoes passing through a model of the 
 
 Fig. li. Photograph of a sound-wave, (I'll', entering a model 
 of the New Theatre, and of the echoes Oi, produced by the 
 orchestra screen, 02 from tlie main floor, (13, from the floor 
 of the orchestra pit, a<, the reflection from the orchestra 
 screen of the wave 03, n^ the wave originating at the edge of 
 the stage. 
 
 theatre by a modification of what may be called the Toeppler-Boys- 
 Foley method of photographing air disturbances. The details of the 
 adaptation of the method to the present investigation will be ex- 
 plained in another paper. It is sufficient here to say that the method 
 consists essentially of taking off the sides of the model, and, as the 
 sound is passing through it, illuminating it instantaneously by the 
 light from a very fine and somewhat distant electric spark. After 
 passing through the model the light falls on a i)hotographic plate 
 placed at a little distance on the other side. The light is refracted by 
 the soimd-wa\'es, which thus act practically as their own lens in pro- 
 ducing the photograph. 
 
 In the accompanying illustrations reduced from the photographs 
 the enframing silhouettes are shadows cast by the model, and all
 
 Fio. 15 
 
 Fig. 1H 
 
 ii; 
 
 Fig. 19 
 
 In.. IT 
 
 I'lu. iO 
 
 Two scries of pholnjjrnplis of the soiiml ami its rt-fliTlions in llir Nrw Tlirnlrr. — 15 lo 17 licfoir, IK to ill oflrr 
 llu* installiitinii (if tin- rnnopy in thrrt-ilinjj. 'I'lic rffit-l of Ihr (-iinopy in pnttit-tinjj ihi* l»ftliMn\'. foyer rhnir^, 
 boxes, nnil the iirrluvilra chairs Imck »f row L is shuuii l>y coniparinK Fi^s. I!) nnil -Ht with Fifts. 10 Ami 17.
 
 Ks> THEATRE ACOUSTICS 
 
 within art' direct photographs of the actual sound-wave and its 
 echoes. For examj)le, Fig. 14 shows in silhouette the principal longi- 
 tudinal section of the main auditorium of the New Theatre. WW is 
 a photograph of a sound-wave which has entered the main auditorium 
 from a jioint on tlie stage at an ordinary distance l)ack of the pros- 
 cenium arch; ch, is tiie reflection from the solid rail in front of the 
 orchestra pit, and Oj, the reflection from the floor of the sound which 
 has passed over the top of the rail; 03 is the reflection from the floor 
 
 Fig. i]. I'liotoKraph of the direct sound, WJV, and of the 
 echoes from the various surfaces; 00,3, a wave, or echo, due 
 to the combination of two waves which originated at the 
 orchestra pit; ci from the oval panel in the ccihng; c^ and 
 Cs. from the ceiling mouldings and cornice over the prosce- 
 nium arch; Ci, a group from the moulding surrounding the 
 panel; Cj, from the proscenium arch; ij, fcj, he from the 
 screens in front, and the walls in the rear of the boxes, 
 balcony and gallery. 
 
 of the pit, and 04 the reflection of this reflected wave from the rail ; 
 while «5 originated at the edge of the stage. None of these reflections 
 are important factors in determining the acoustical quality of the 
 theatre, but the photograph affords excellent opportunity for show- 
 ing the manner in which reflections are formed, and to introduce the 
 series of more significant photographs on page 181. 
 
 Figures 15, 16, and 17 show the advance of the sound through the 
 auditorium at .07, .10, and .14 second intervals after its departure
 
 THEATRE ACOUSTICS 183 
 
 from the source. In Fig. 15, the waves wliicli originated at the 
 orchestra ])it can be readily distinguished, as well as the nascent 
 waves where the i)riinary sound is striking the ceiling cornice imme- 
 diately over the prosceniiun arch. The proscenium ardi itself was 
 very well designed, for the sound passed i)arallel to its surface. 
 Otherwise reflections from the proscenium arch wouUl also have 
 shown in the photograj)!!. These would lia\ c heen directed toward 
 tlie audience and miglit have heen very perceptible factors in deter- 
 mining the ultinuite acoustical quality. 
 
 The system of reflected waves in the succeeding photograph in 
 the series is so complicated that it is difficult to identify the several 
 reflections by verbal descrijjtion. The i)hotogra])h is, therefore, re- 
 produced in Fig. '■21, lettered and with accompanying legends. It is 
 interesting to observe that all the reflected waves which originated 
 at tlie orchestra pit have disappeared with the exception of waves 
 Uo and a.i. These have combined to form practically a single wave. 
 Even this combined wave is almost negligible. 
 
 The acoustically important reflections in the vertical section are 
 the waves Ci, c^, and c^. The waves 6i and b^ from the screen in front 
 of the boxes and from the back of the boxes are also of great impor- 
 tance, but the peculiarities of these waves are better shown by photo- 
 graphs taken vertically through a horizontal .section. 
 
 The waves Ci, Co, Ca, and bi and bo show in a striking maniuT the 
 fallacy of tlie not uncommon representation of the propagation of 
 sound by straight lines. For example, the wave Ci is a reflection from 
 the oval j)anel in the ceiling. The curvature of this ])anel is such 
 that the ray construction would give i)ractically parallel rays after 
 reflection. Were the geometrical representation by rays an ade- 
 quate one the reflected \\ ave would thus be a flat disc e<iual in area 
 to the oblique projection of the ])anel. As a matter of fact, however, 
 the wave sjjreads far intcj the geometrical shallow, as is shown by 
 the curved i)ortion reaching well out toward the proscenium arch. 
 Again, waves r„ and Ci are ri-fleclions from a cornice whose irregular- 
 ities are not so oriented as to suggest by the simple geometrical 
 representation of rays the formation of sucli waves as are here clearly 
 shown. Hut each >mall cornice moulding originates an alnu).sl hemi- 
 spherical wave, and llie mouldings are in two grou|)s, the ])osition of
 
 184 THEATRE ACOUSTICS 
 
 each being such tliat the spherical waves conspire to form these two 
 master waves. The inadeciuacy of the discussion of the subject of 
 architectural acoustics by the construction of straight lines is still 
 further shown by the waves reflected from the screens in front of the 
 boxes, of the balcony, and of the gallery. These reflecting surfaces 
 are narrow, but give, as is clearly seen in the photograph, highly 
 divergent waves. This spreading of the wave beyond the geometrical 
 projection is more pronounced the smaller the opening or the reflect- 
 ing obstacle and the greater the length of the wave. The phenom- 
 enon is called diffraction and is, of course, one of the well-known 
 phenomena of physics. It is more pronounced in the long waves of 
 sound than in the short waves of light, and on the small areas of an 
 auditoriimi than in the large dimensions of out-of-door space. It 
 cannot be ignored, as it has been heretofore ignored in all discussion 
 of this phase of the problem of architectural acoustics, with im- 
 punity. The method of rays, although a fairly correct approximation 
 with large areas, is misleading under most conditions. For example, 
 in the present case it would have predicted almost perfect acoustics 
 in the boxes and on the main floor. 
 
 Figures 17 and 20 show the condition in the room when the main 
 sound-wave has reached the last seat in the top gallery. The wave 
 Ci has advanced and is reaching the front row of seats in the gallery, 
 producing the effect of an echo. Alittle later it will enter the balcony, 
 producing there an echo greater in intensity, more delayed, and 
 affecting more than half the seats in the balcony, for it will curve 
 under the gallery, in the manner just explained, and disturb seats 
 which geometrically would be protected. Still later it will enter the 
 foyer seats and the boxes. But the main disturbance in these seats 
 and the boxes, as is well shown by the photograph, arises from the 
 wave Ci, and in the orchestra seats on the floor from the wave Cz. 
 
 In the summer following the opening of the theatre, a canopy, 
 oval in plan and slightly larger than the ceiling oval, was hung from 
 the ceiling surrounding a central chandelier. The effect of this in 
 preventing these disturbing reflections is shown by a comparison, 
 pair by pair, of the two series of photographs, Figs. 15 to 17 and 
 Figs. 18 to 20. It is safe to say that there are few, possibly no 
 modern theatres, or opera houses, equal in size and seating capacity,
 
 I'll; ii Fio. ii 
 
 on 
 
 Fio. <a t Hi- >!•* 
 
 an 
 
 lie, n 1 1... it: 
 
 Pliotof^a|>lis slinwiiiK ll'c rfflwlimm. in ii viTti<-al plane, from tlic siilca of ihc prusiTiiium 
 anil, till- iiluiii Willi lirliiw llir iirtnrs' Imix. iiiiil llir rail or scrrrn in front of the Uixrs. 
 Tlio |ilioto(;ni|ili» takni in nniiu'riial sitnirnn- allow tin- (ironrrss of n single mmuil-wavc 
 and it.t ri'llotions.
 
 18C THEATRE ACOUSTICS 
 
 whicli arc so free from this parlicular type of disturbance as the New 
 Theatre at the present time. 
 
 In the study of the New Theatre, photographs were taken through 
 several horizontal sections. It will l)e sufficient for the purposes of 
 the present jjaper to illustrate the effect of curved surfaces in pro- 
 ducing converging waves by a few photograjjhs showing the propa- 
 gation of sound through a single section in a plane passing through 
 the parapet in front of the boxes. The reflected waves shown in 
 
 Fig. 'is. A photograpli. one uf luanv takon, showing 
 in vertical section one stage of tlie reflection 621 
 Fig. 21. These reflections were eliminated by the 
 arcliilects in the summer following the opening 
 of the theatre, but have been in part restored by 
 subsequent changes. 
 
 Fig. 22 originating from the edge of the proscenium arch and from 
 the base of the column can be followed throughout all the succeeding 
 photographs. In Fig. 23 are shown waves originating from the plain 
 wall beneath the actor's box and the beginning of some small waves 
 from the curved parapet. It is easily possible, as it is also interesting 
 and instructive, to follow these waves through the succeeding photo- 
 graphs. In Fig. 25 the sound has been reflected from the rear of the 
 parajict; while in Fig. 26 it has advanced further down the main 
 floor of the auditorium, narrowing as it proceeds and gaining in in- 
 tensity. The waves reflected from the parapet outside of the aisles 
 are here shown approaching each other behind the wave which has 
 been reflected from the parapet between the aisles. Waves are also 
 shown in Fig. 26 emerging from the passages between the boxes.
 
 THKATRE ACOI'STICS 187 
 
 Indeed, it is possible to trace the waves arising from a second reflec- 
 tion from tlie proscenium arch of the sound wliich, first reflected 
 from the corresponding surfaces on the other side, has crossed di- 
 rectly in front of the stage. With ;i lilll<- care, it is possible also to 
 identify tliese waves in tlie last ])h()t(ij,'r:i])h. 
 
 Altliough many were taken, it will sufhci- to sliow a single jjlioto- 
 graph. Fig. 28, of the reflections in the jilane passing through the 
 back of the boxes. These disturbing reflections were almost entirely 
 eliminated in the revision of the theatre by the removal of the boxes 
 from the first to the second row and by utilizing the s])ace vacated 
 logetlier with the anterooms as a single l)alcony filled witli seats. 
 
 An excellent illiLstration of tiie use of such photograjjhs in plan- 
 ning, before construction and while all the forms are still fluid, is to 
 l)e found in one of the tlieatres now ixMUg built in Boston by Mr. 
 C. II. Blackall, who has had an excei)tionally large and successful 
 experience in theatre design. The initial pencil sketch. Fig. 29, gave 
 in the model test the waves shown in the progressive series of photo- 
 graphs. Figs. .'51 to fi^. The ceiling of interix-netrating cylinders was 
 then changed to the form shown in finished section in Fig. :>(•, with 
 the residts strikingly indicated in the i)arallel series of photographs, 
 Figs. 34 to 36. It is, of course, easy to identify all tiie reflections in 
 each of the.se photographs, — the reflections from the ceiling aiul tlie 
 balcony front in the first ; front the ceiling and from both the balcony 
 and gallery front in the secoiul; and in the third ])li()t<)graph of the 
 series, the reflections of the ceiling reflection fmm ll\e balcony and 
 gallery fronts and Iroiii I Ik floor. I?ul the es.sential point to be ob- 
 served, in coinjiaring the two series ])air by pair, is the almost total 
 ab.sence in the second .series of the ceiling echo and the nlativcly 
 clear condition back of the advancing sound-wave. 
 
 CONSOXANCK 
 
 Con.sonance is the process whereby, due to >uital>ly i)laced rtllect- 
 ing walls, "(he voice is sui)iiorled and >trenglheiu'«l." It is the one 
 acoustical virtue liiat is |iositive. It i^ al-o tin- characlerislic virtue 
 of the nuxlern theatre, and that througii which this complicate*! 
 auditoriinn suruKumts the at Iriidant evils of interference, reverbi-ra- 
 lion. and echo. Yet such i> our nnxlrrn analv si> of the prol)Uui tluit
 
 188 
 
 THEATRE ACOUSTICS 
 
 \vc cU) not t'vt-n havi- for it a nanu-. On the other liand. it is the virtue 
 which tlie Clreek theatre has in least degree. It is, therefore, all the 
 more interesting that it should have been included in the analysis of 
 Vitruvius, and should have received a name so accurately descriptive. 
 Indeed, one can hardly make exjilanation of the phenomenon better 
 than through the very type of theatre in which its lack is the one 
 admitted defect. 
 
 The Greek theatre enjoys a not wholly well-founded reputation 
 for extremely good acoustics. In most respects it is deserved; but 
 
 Fig. 29. Section in pencil sketcli of Scollay Square Theatre, Boston. 
 Mr. C. H. Blackall, Architect. 
 
 the careful classical scholar, however gratified he may be by this 
 praise of a notable Greek invention, regards himself as barred by 
 contemporaneous evidence from accepting for the theatre imr(uali- 
 fied praise. E^'ery traveler has heard of the remarkable quality of 
 these theatres, and makes a trial wherever opportunity permits, be 
 it at beautiful Taormina, in the steep sloped theatre at Pompeii, the 
 great theatre at Ephesus, or the "little theatre" on the top of Tus- 
 culum, — always with gratifying results and the satisfaction of hav- 
 ing confirmed a well-known fact. Perhaps it is useless to try to 
 traverse such a test. But there is not a theatre in Italy or Greece 
 which is not in so ruined a condition today that it in no way what- 
 ever resembles acoustically its original form. If its acoustics are
 
 THEATRE ACOl STICS 
 
 189 
 
 perfect today, they certainly were not originally. Complete " scaena " 
 and enclosing walls distinctly altered the acoustical conditions. The 
 traveler has in general tested what is little more than a depression 
 in the ground, or a hollow in a f|uict country hillside. As a matter of 
 fact, the theatre in its original form was better than in its ruined 
 state. Still, witli all its excellencies it was not wholly good. Its 
 acoustical qualities were not wholly acceptable to its contemporaries. 
 
 Fio. 80. Finislicil sirtimi nf Stulluy Sqiiare Tlieutrt'. Bosloii.^ Mr. C. H. Blackiill. .\nliitoct. 
 
 and would be less acceptable in a mddfiii tlu-atre, and for modern 
 drama. 
 
 Thf (liflicuitN' witli nucIi casual evidence is that it is gathered 
 umlcr wholly al>n(>rmal coiulilions. Not only arc the ruins l)ut scant 
 reminders of the original structure, but the absence of a large audi- 
 ence vitiates the test, as it would vitiate a test of any modern theatre. 
 But while in a modern anditoriMin llie presence of an audii-nce almost 
 always, though not invariably, imjjroves liie acoustics, in the classical 
 theatre the presencv of an audience, in so far us it has any effect, is
 
 190 THKATRE ACOUSTICS 
 
 disadvantageous. The effect of an audience is always twofold, — it 
 diminishes the rever])eration, and it diminishes the loudness or in- 
 tensity of the voice. In general, the one effect is advantageous, the 
 other disadvantageous. But in the Greek theatre, occupied or un- 
 occu])ied, ruined or in its original form, there was very little rever- 
 beration. In fact, this was its merit. On the other hand, the very 
 fact that there was little reverberation is significant that there was 
 very slight architectural reenforcement of the voice. One might well 
 be unconvinced l)y such a priori considerations were there not ex- 
 cellent evidence that these theatres were not wholly acceptable 
 acoustically even in their day, and for drama written for and more 
 or less adapted to them. Excellent e\'idence that there was insuffi- 
 cient consonance is to be found in the megaphone mouthpieces used 
 at times in both the tragic and the comic masks, and in the proposal 
 by \'itruvius to use resonant vases to strengthen the voice. 
 
 The doubt is not as to whether a speaker, turned directly toward 
 the audience and speaking in a sustained voice, could make himself 
 heard in remote parts of a crowded Greek theatre. It is almost cer- 
 tain that he could do so, even in the very large and more nearly level 
 theatres, such as the one at Ephesus. Better evidence of this than 
 can be found in the casual test of a lonely ruin is the annual per- 
 formance by the staff of the Comedie Frangaise in the theatre at 
 Orange. But even this, the best preserved of either Greek or Roman 
 theatres, is but a ruin, and its temporary adaptation for the annual 
 performance is more modern than classical. A much better test is in 
 the exercises regularly held in the Greek Theatre of the University of 
 California, designed by ]Mr. John Galen Howard, of which President 
 ^^heeler speaks in most approving terms. The drama, especially 
 modern drama, differs from sustained speech and formal address in 
 its range of utterance, in modulation, and above all in the require- 
 ment that at times it reaches the audience with great dynamic quality 
 but without strain in enunciation. Mere distinctness is not sufficient. 
 It was through a realization of this that the megaphone mouthpiece 
 was invented, — awkward in use and necessarily destructive of many 
 of the finer shades of enunciation. That it was only occasionally used 
 proves that it was not a wholly satisfactory device, but does not de- 
 tract its evidence of weakness in the acoustics of the theatre.
 
 Via. 'M 
 
 Fig. S4 
 
 Via. 33 
 
 Fio. 3« 
 
 Two series of plintoKraphs slmwiDR. Figs. 31-33. the rcfloelions whicli would li«vf rrsuUeil from the exe- 
 riitinn of tlio first poncil aki-trli of tlic Scollay Sqiion- Tliriitrp [Vig. Ht). and. Kiss. M-SO. from the 
 execution of the second !ikclch liy Mr. Blacluill (shown in linishol section in V'lg. 30).
 
 19'^ THEATRE ACOUSTICS 
 
 The megaphone mouthpiece bears to the acoustics of the Greek 
 theatre tlie same evidence, only in a reciprocal form, that the mask 
 itself bears to the theatre's illumination. It was not possible to see 
 in bright daylight, particularly in the bright sunlight of the Mediter- 
 ranean atmosphere, with anything like the accuracy and detail pos- 
 sible in a darkened theatre with illuminated stage. The pupil of the 
 eye was contracted, and the sensitiveness of the retina exhausted by 
 the brilliancy of the general glare. Add to this that the distance from 
 the stage was very much greater in the Greek than in the modern 
 theatre, audience for audience, and one can realize the reason for the 
 utter impossibility of facial expression in Greek dramatization except 
 by artificial exaggeration. The hea\'iness and inflexibility of these 
 devices, and, therefore, their significance as proof of some inherent 
 difficulty in dramatic presentation, is emphasized by the delicacy of 
 line and fine appreciation of the human form shown in other con- 
 temporaneous art. 
 
 Not less significant in regard to the acoustics of the Greek theatre 
 are the directions given by Vitruvius for the reenforcement of the 
 voice by the use of resonant vases : 
 
 " Accordingly bronze vessels should be made, proportional in size to the 
 size of the theatre, and so fashioned that when sounded they produce with 
 one another the notes of the fourth, the fifth, and so on to the double octave. 
 These vessels should be placed in accordance with musical laws in niches 
 between the seats of the theatre in such position that they nowhere touch 
 the wall, but have a clear space on all sides and above them. They should 
 be set upside down and supported on the side facing the stage by wedges not 
 less than half a foot high. . . . With this arrangement, the voice, spreading 
 from the stage as a center, and striking against the cavities of the different 
 vessels, will be increased in volume and will wake an harmonious note in 
 unison with itself." 
 
 There is good reason for believing that this device was but very 
 rarely tried. This, and the fact that it could not possibly have ac- 
 complished the purpose as outlined by Vitruvius, is not germane. 
 The important point is that its mere proposal is evidence that the 
 contemporaries of the Greek theatres were not wholly satisfied, and 
 that the defect was in lack of consonance. 
 
 It would be inappropriately elaborate and beyond the possible 
 length of this paper to give in detail the method of calculating the
 
 THEATRE ACOITSTICS 193 
 
 loudness of sound in ditJVrful parts of an auditorium. That suhjt-ft 
 is reserved for anotlier paper in preparation, in which will be given 
 not merely the method of calculation but the necessary tables for its 
 simplification. It i.s, however, possible and proper to give a general 
 statement of the principles and processes involved. 
 
 In this discussion I shall leave out as already adequately discussed 
 the phenomenon of interference, or rather shall dismiss the subject 
 with a statement that when two sounds of the same pitch are super- 
 posed in exact afjreeinent of i)liase, the intensity of the soimd is the 
 square of tlie sum of the stjuare roots of their separate intensities; 
 when they are in opposite phases, it is the square of the difference of 
 the square roots of their intensities; but when several sounds of the 
 same j)itch arrive at any \nnnt in the room with a random difference 
 of phase their probable intensity is the simple numerical sum of their 
 separate intensities. It is on the assumption of a random difference 
 of phase and an average probable loudness that I shall here consider 
 the question. This has the advantage of being the simijler and also a 
 first a])i)roximati<)n in an auditorium designed for articulate si)eech. 
 
 When sound spreads from a spherically symmetrical source it 
 diminishes as the square of the distance. When the sound is being 
 projjagated, still in space unrestricted by walls or ceiling, but over 
 the heads of a closely seated audience, the law of the dnninution of 
 the sound is more rapid than the law of the inverse square. This more 
 rapid diminution of tiie sound is due to the absorption of the sound 
 by the audience. It is a function of the elevation of the speaker and 
 the angle of inclination of the floor,^ — in other words, the angle be- 
 tween the sight lines. The diminution of the intensity of lii<> sound 
 due to distance is less the greater this angle. 
 
 If the auditorium be enclosed by not too remote walls, the voice 
 coming directly from the sj)eaker is reenforced by the reflection from 
 the retaining walls. However, it is obvious that the sounds reflected 
 from the walls and ceilings have traversed greater paths than the 
 .sound of the voice which has come directly. If this ditference of i)atli 
 length is great, the .sounds will not arrive simultamx>usly. If, i>ow- 
 ever, the i)ath differeiurs are not great, the reflected sounds will 
 arrive in time to reenforce the voice which has come directly, each 
 svllal)le l)V itself, or, indt-ed, in lime for the .self support of the sub-
 
 194 
 
 THKATRE ACOUSTICS 
 
 syllaliic compoiuMits. It is to tliis mutual strengthening of concur- 
 rent sounds within eacli ek'nient of articulate speech that Vitruvius 
 has given the name "consonance." 
 
 Thus in the computation of the intensity of the voice which has 
 come directly from the speaker across the auditorium, it is necessary 
 to take into consideration not merely the duiiiuution of intensity 
 according to the law of the inverse square of the distance and the 
 diminution of the intensity due to the absorption by the clothing of 
 
 Fig. 37 
 
 Tlie Harris Theatre, Minneapolis, first design. 
 Chapman and Magnej, Architects. 
 
 the audience, but also, as a compensating factor for the latter, the 
 diffraction of the sound from above which is ever supplying the loss 
 due to absorption, while in computing the intensity of the sound re- 
 flected from any wall or other surface one must take into considera- 
 tion all this, and also the coefficient of reflection of the wall and the 
 diffraction due to the restrictea area of the reflecting element. 
 
 Abstract principles are sometimes tedious to follow even when 
 not difficult. In Fig. 38 is shown a photograph taken in an investiga- 
 tion for the architects, Messrs. Chapman and Maguey, of the Harris 
 Theatre, to be erected in Minneapolis, which affords an excellent 
 example of both favorable and unfavorable conditions in respect to 
 consonance. The initial sketch for this theatre offered no problems
 
 THEATRE ACOUSTICS 19.5 
 
 either of interference or reverberation, and of echo only in the hori- 
 zontal section. The only very considerable question presented by the 
 plans was in respect to consonance and lliere in regard only to the 
 more remote parts of the floor and of tiie balcony. 'I'lie particular 
 photograph here reproduced records the condition of the sound in 
 the room at such an instant as to bring out this aspect of the problem 
 in marked degree. 
 
 The forward third of the l)akony in this theatre affords an ex- 
 cellent example of consonance, for the reflection from the ceiling 
 arrives so nearly simultaneously with the sound which has come 
 
 Fig. 38. Sliow lug the foiisonaiur In llu' bnli-oiiv df llic Harris 
 Theatre. This relates only to ronsonanre in the vfrtical 
 section. 
 
 directly from the stage as to "strengthen and sni)porl " it and yet 
 "leave the words clear and distinct." The interval between the two, 
 the direct and the reflected voice, varies from .01 second to .03 
 second. Back of the first thirtl. however, the consonance from the 
 ceiling gradually diminishes and is practically imperceptible beyoiul 
 the middle of tin- galK'iy. Hack of that i)oint the direct voice di- 
 minishes ra])i<lly since it is j)assing in a confined space over the highly 
 absorbent clothing of the audience. The loss of intensity at Uie rear 
 of the gallery is increased by tiie carrying of the hori/.cntal portion 
 of the ceiling so far rearward. While the effect of this is to throttle 
 the rear ol the galU-ry it obviously strengthens the voice in the for- 
 ward third. Although there is thus some compen.sation, on the 
 whole the forward |)art of the gallery din-s not need this service so
 
 196 THEATRE ACOUSTICS 
 
 mucli as the rear seats. The photograph shows this process clearly: 
 the main sound-wave can be seen advancing after having passed the 
 angle in the ceiling. The wave reflected from the ceiling can be seen 
 just striking the gallery seats. It is evident that at the instant at 
 which tiic photograjjli was taken the sound-wave was receiving the 
 last of this sui)port by the sound reflected from the ceiling. 
 
 The photograph also shows how the sound after passing the ceil- 
 ing angle spreads into the space above, thus losing for the moment 
 thirty jjor cent of its intensity, a loss, however, to be regained in 
 considerable part later. 
 
 On the main floor the reflection from the ceiling strengthens the 
 direct voice only for the long syllabic components. Nevertheless, in 
 comparison with other theatres the forward part of the floor of this 
 theatre will be excellent. There will be just a trace of echo immedi- 
 ately under the front of the balcony, but this will be imperceptible 
 beyond the first four rows of seats under the balcony. It is obvious 
 from the photograph that there is no consonance in the rear of the 
 main floor of the auditorium under the balcony. 
 
 A not unnatural, certainly a not uncommon, inquiry is for some 
 statement of the best height, the best breadth, and the best depth for 
 a theatre, for a list of commended and a list of prohibited forms and 
 dimensions. A little consideration, however, will show that this is 
 neither a possible nor the most desirable result of such an inves- 
 tigation. 
 
 For a simple rectangular auditorium of determined horizontal 
 dimensions there is a best height. TMien, however, the horizontal 
 dimensions are changed the desirable height changes, although by no 
 means proportionally. When the floor is inclined, when the walls are 
 curved, when there are galleries and connection corridors, when the 
 material of construction is varied in character, the problem becomes 
 somewhat more intricate, the value of each element being dependent 
 on the others. Moreover it is futile to attempt to formulate a stand- 
 ard form even of a single tj-pe of auditorium. How greatly the 
 design must vary is well illustrated in the four theatres which have 
 been taken as examples, ^ the Little Theatre with all the seats on 
 the main floor, the Harris Theatre, very long, very broad, and with
 
 THEATRE ACOUSTICS 197 
 
 but a single gallery, the ScoUay Square Theatre with two galleries, 
 and the New Theatre with two rows of boxes and two galleries. 
 The fundamental conditions of the problem, not the entirely free 
 choice of the architect, determined the general solution in each 
 case. Acoustical quality is never the sole consideration; at best it 
 is but a factor, introduced sometimes early, sometimes late, into 
 the design.
 
 8 
 BUILDING MATERIAL AND MUSICAL PITCH' 
 
 1 HE iihsorbing power of the vtirious materials that enter into 
 llic construction and fiirnishinfj of an auditoriinn is but one phase 
 in the general investigation of the subject of architectural acoustics 
 which the writer has been prosecuting for the past eighteen years. 
 During the first five years the investigation was devoted almost 
 exclusively to the determination of the coefficients of absorption 
 for sounds having the i)itch of violin C (51-2 vibrations per second). 
 The results were published in the American Architect and the En- 
 gineering Record in 1900.' It was obvious from the beginning that 
 an investigation relating only to a single pitch was but a preliminary 
 excursion, and that the comjjiete solution of the problem called for 
 an extension of the investigation to cover tiie whole range in pitch 
 of the sp<Mking xoice and i>l' I lie musical scalr. Tlierefore during 
 the years wliich have since elapsed the investigation hiis been ex- 
 tended over a range in pitch from three octaves below to three 
 octaves above violin ('. That it luus taken so long is due to the fact 
 that other aspects of the acoustical problem also pressed for solu- 
 tion, such for example as those depending on form, — interference, 
 resonance, and echo. The delay has also been due in i)art to the 
 nature of the investigation, which has necessarily been opportunist 
 in character and. given every opportunity, somewhat laborious and 
 exhausting. Some meiusure of the labor involved may be gained 
 from the fact that the investigation of tlir absorjjlion coefficients 
 for the single note of violin (' re(|uired evrry other night from twelve 
 until livt- for a period of three years. 
 
 While many improvements have been made in the inetlioii> of 
 investigation and in IIk' iipparalns employed since the first paper 
 was pul)Iished fourteen years ago. the proenl paper is devoted solely 
 to the presentation of the re>nll>. I shall venture to di.seu.ss, al- 
 though briefly, the circmnstances under which the measurements 
 
 ' Tlic HrickbuiUlir. vol. xxiii, no. 1, Jomuiry. 1914. ' .N". 1. p I- 
 
 IN
 
 200 BUILDING MATERIAL 
 
 were inado, my ol^ject heinfj to so interest architects that they will 
 call attention to any opportunities which may come to their notice 
 for the further extension of this work; for, while the absorbing 
 powers of many materials have already been determined, it is 
 evident that the list is still incomplete. For example, the coefficient 
 of glass has been determined only for the note first studied, C, an 
 octave above middle C. In 1898 the University had just com- 
 pleted tlie construction of some greenhouses in the Botanical 
 Gardens, which, before the plants were moved in, fulfilled admirably 
 the conditions necessary for accurate experimenting. Glass formed 
 a very large part of the area of the enclosing surfaces, all, in fact, 
 except the floor, and this was of concrete whose coefficient of absorp- 
 tion was low and had already been determined with accuracy. By 
 this good fortune it was possible to determine the absorbing power 
 of single-thickness glass. But at that time the apparatus was adapted 
 only to the study of one note; and as the greenhouse was soon fully 
 occupied with growing plants which could not be moved without 
 danger, it was no longer available for the purpose when the scope 
 of the investigation was extended. Since then no similar or nearly 
 so good opportunity has presented itself, and the absorbing power 
 of this important structural surface over the range of the musical 
 scale has not as yet been determined. There was what seemed for 
 the moment to be an opportunity for obtaining this data in an in- 
 door tennis court which Messrs. McKim, Mead and ^Miite were 
 erecting at Rhinebeck on the Hudson, and the architects undertook 
 to secure the privilege of experimenting in the room, but inquiry 
 showed that the tennis court was of turf, the absorption of which 
 was so large and variable as to prevent an accurate determination 
 of the coefficients for the glass. The necessary conditions for such 
 experiments are that the material to be investigated shall be large 
 in area, and that the other materials shall be small in area, low in 
 power of absorption, and constant in character; while a contribut- 
 ing factor to the ease and accuracy of the investigation is that the 
 room shall be so located as to be very quiet at some period of the 
 day or night. The present paper is, therefore, a report of progress 
 as well as an appeal for further opportunities, and it is hoped that 
 it will not be out of place at the end of the paper to point out some
 
 AmsiCAL PITCH 201 
 
 of the problems which remain and ask that interested architects 
 call attention to any rooms in which it may be possible to complete 
 the work. 
 
 The investigation does not wholly wait an opportunity. A 
 special room, exceptionally well adapted to tlie i)urpose in size, 
 shape, and location, h;is been constantly available for the research 
 in one form or another. This room, initially lined with brick set 
 in cement, has been lined in turn with tile of various kinds, with 
 plaster, and with plaster on wood lath, as well as finished from time 
 to time in other surfaces. This process, however, is expensive, and 
 carried out in completeness would be beyond what could be borne 
 personally. Moreover, it has further limitations. For example, it 
 is not possible in this room to determine the absorbing power of 
 glass windows, for one of the essential features of a window is that 
 the outside space to which the sound is transmit led siiall be open 
 and unobstructed. An inner lining of glass, even though this be 
 placed several inches from the wall, wuul<l not with certainty repre- 
 sent normal conditions or show tlic cfrcct of windows as ordinarily 
 employed in an auditorium. Notwithstanding these limitations, 
 this room, carefully studied iti respect to the effects of its pecu- 
 liarities of form, especially such as arise from interference and reso- 
 nance, has been of great service. 
 
 W.\LL AND CeILING-SuRF.\CES 
 
 It is well to bear in mind that the absorption of sound by a wall- 
 surface is structural and not superficial. That it is sujjerficial is one 
 of the most wi(lcs])rca<l and persistent fallacies. When this investi- 
 gation wjui initially undertaken in an endeavor to correct the 
 acoustics in the lecture-room of the Fogg .\rt Mu.seum, one of the 
 first suggestions was that IIh' walls wcit loo >niootli and should l)e 
 roughened. The proposal al llial lime was that the walls be re- 
 plastered and scarred with tlir toothed trowel in a swirling motion 
 and then i)ainted, a type of deeoraticm common twenty years ago. 
 A few years later incjuiries were received in regard to sanded >ur- 
 faces, and still later in regard to a rough, pebbly surface of un- 
 troweled plaster; while within the past three years there have been 
 many in(juiries as to the eilieieney of roughened brick or «>f rough
 
 i202 BUILDING MATERIAL 
 
 lu'Wii stone. On tlie general principle of investigating any proposal 
 so long as it conlainetl even a jjossihijity of merit, these suggestions 
 were put to test. The concrete floor of a room was covered with a 
 gravel so sifted that each pebble was about one-eighth of an inch 
 in diameter. This was spread oviT the floor so that jx'bhle touched 
 pebble, making a layer of but a single pebble in thickness. It 
 showed not the slightest absorbing power, and there was no per- 
 ceptible decrease in reverberation. The room was again tried with 
 sand. ()f course, it was not possible in this case to insure the thick- 
 ness of a single grain only, but as far as possible this was accom- 
 plished. The result was the same. The scarred, the sanded, the 
 pebbly plaster, and the rough hewn stone are only infinitesimally 
 more efficient as absorbents than the same walls smooth or even 
 polished. The failure of such roughening of the wall-surfaces to 
 increase either the absorption or the dispersion of sound reflected 
 from it is due to the fact that the sound-waves, even of the highest 
 notes, are long in comparison with the dimensions of the irregu- 
 larities thus introduced. 
 
 The absorption of sound by a wall is therefore a structural 
 phenomenon. It is almost infinitely varied in the details of its 
 mechanism, but capable of classification in a few simple modes. 
 The fundamental process common to all is an actual yielding of the 
 wall-surface to the vibrating pressure of the sound. How much the 
 wall itields and what becomes of the motion thus taken up, depends 
 on the nature of the structure. The simplest type of wall is obvi- 
 ously illustrated by concrete without steel reenforcement, for in 
 this there is the nearest approach to perfect homogeneity. The 
 amount that this wall would yield would depend upon its dimen- 
 sions, particularly its thickness, and upon the density, the elasticity, 
 and the viscosity of the material. It is possible to calculate this 
 directly from the elements involved, but the process would be 
 neither interesting nor convincing to an architect. It is in every 
 way more satisfactory to determine the absorbing power by direct 
 experiment. A concrete wall was not available. In its stead, the 
 next more homogeneous wall was investigated, an eighteen-inch 
 wall of brick set in cement. This wall was a very powerful re- 
 flector and its absorbing power exceedingly slight. Without going
 
 MITSICAL PITCH 203 
 
 into Lhc dt'lails of tlu- cxptiiiiK-nl, it will suffice here to say that 
 this wall absorbed one and one-tenth per cent of the lowest note 
 investigated, a C two octaves below middle C, having a vibration 
 frequency of sixty-four per second; one and two-tenths per cent 
 of sounds an octave in pitch higlur; one and four-tenlhs per cent 
 of sounds of middle C; one and seven-tenths per cent for violin ("; 
 two per cent for sounds having a pitch one octave above; two and 
 three-tenths for two octaves above; and two and one-half per cent 
 for sounds having a pitch three octaves above violin C, that is to 
 say, 4094 vibrations per second, the highest note investigated. 
 These may be WTitten as coefficients of absorption thus: 
 
 C, .011; Co, .012; C3, .014; C4, .017; C5, .020; C,, .023; C,, .025. 
 
 There is a graphical niclhod of presenting these results which is 
 always employed in physics, and frequently in other branches of 
 science, when the i)lienomenon under investigation is simjjly pro- 
 gressive and dependent upon a single variable. Whenever these 
 conditions are satisfied — and they are usually satisfied in any 
 well conducted investigation the grajjhical re[)resentation of 
 the results takes the form of a diagram in which tlie n-sults of the 
 measurements are plotted vertically at horizontal distances de- 
 termined by the variable condition. Thus in the following diagram 
 (Curve 1, Fig. 1) the coi'liicients of absorption are ])lotted vertically, 
 the varying pitch being represented by horizontal distances along the 
 base line. Such a diagrammatic representation serves to reveal the 
 accuracy of the work. If the phenomenon is a continuous one, 
 the plotted points should lie on a smooth curve; the nearness with 
 which they do .so is a measure of the accuracy of the work if the 
 points thus plotted an- determined 1>\ tiitircly independent experi- 
 iiiiiils. This form of diagranuuatic representation serves another 
 piir|)ose in i)ermitting of the convenient interpolation for values 
 intermediate between observed values. 'I'lie coeiiicients f»)r each 
 type of wall-surface will be given i>olh numerically and diagram- 
 matically. In onlt r lo avoid confusion, the ob-served points have 
 been indicated oidy on the curve for wood sheathing in Fig. 1. It 
 will suffice to say merely that the other curves on this diagram 
 are drawn accurately through the plotted observations.
 
 ^204 
 
 Bl ILDING INIATERIAL 
 
 The next wall-surface investigated was jilaster on hollow terra 
 cot I a tile. Tlie plaster coat was of gjpsuni hard plaster, the rough 
 phuster being five-eighths of an inch in thickness. The result shows 
 a slightly greater absorption due to the greater flexibility of a hollow 
 
 10 
 
 
 c, 
 
 a 
 
 c, 
 
 c 
 
 c„ 
 
 Fig. 1. Absorbing power for sounds varying in pitch 
 from C = 6i to C = 4,090; 1, brick wall; 2, plaster 
 on terra cotta hollow tile; 3, plaster on wire lath; 
 4, same with skim coat; 5, wood sheathing. 
 
 tile wall rather than to any direct effect of the plaster. The differ- 
 ence, however, is not great. The numerical results are as follows 
 (Curve 2, Fig. 1): 
 
 Ci, .012; Ci, .013; Cs, .015; C4, .020; C^, .028; Ce, .040; C7, .050. 
 
 Ci is the lowest note, 64 vibrations per second; C7, the highest, 
 4,096 per second; the other notes at octave intervals between.
 
 MISICAL PITCH 205 
 
 Plaster on an otherwise homogeneous sustaining wall is a first 
 step in the direction of a compound wall, l)ut a vastly greater step 
 is taken when the plaster instead of being applied directly to the 
 sustaining wall is furred to a greater or less distance. In a homo- 
 geneous wall, the absorption of sound is jjartially by connnunication 
 of the vibration to the material of the wall, whence it is tele|)honed 
 throughout the structure, and partlv b\- a yieliling of the wall as a 
 whole, the sound bi-ing then comnuuiicatcd to outside space. In 
 a compound wall in which the exposed surface is furred from the 
 main structure of the wall, the former vibrates between the furring 
 strips like a drum. Such a surface obviously yields more than woultl 
 a surface of plaster applied directly to tile or brick. The energy- 
 which is thus absorbed is partly dissipated l)y the viscosity of the 
 plaster, partly by transmission in the air space behind it, and partly 
 through the furring strips to the main wall. The mechanism of 
 this process is interesting in that it shows how the free standing 
 plaster may absorb a great amount of sound and may present a 
 greater j)ossibility of resonance and of selec-tive absorption in the 
 different registers of pitch. It is obvious that we are here dealing 
 with a problem of more complicated aspect. It is conceivable 
 that the absor|)tion coefficient should dejjend on the naturt> of the 
 supjjorting construction, whether wood lath, wire lath, or expandetl 
 metal lath; on the distance apart of the studding, or the de|)th of 
 the air space; or, and i \<ii more decidedly, on the nature of the 
 plaster emi)loyetl, whether tiie old lime |)las(er or the modern ([uick 
 setting gypsum plaster. A start has been made on a stu(l\' of this 
 problem, but it is not as yet so far ailvanced as to [x-rmit of a system- 
 atic correlation of the results. It nuist suffice to present here the 
 values for a single construction. The most interesting case is that 
 in which lime |)laster Wius ai)plied to wood lath, on wood studding 
 at fourteen-inch spacing, forming a two-inch air space. The co- 
 efficients of al)sorption before the finishing coat wsis put on were 
 (Curve 3, Kig. 1): 
 
 Ci, .048; Ci. MO; C,, .024; C4, .034; C». .030; C«, .0«8; Ct. .043. 
 
 The values ;iflrr the finishing coat was put on were as follows 
 (Curve 4, dotted, I'ig. 1): 
 
 C„ .080; C„ .OW; C3. .OKJ; C«. .018; C., .045; C„ .0^8; (;, .0.>5.
 
 206 BIILDIXG :MATERIAL 
 
 It should he iTinarkccl that the determination of these coefficients 
 was made witliin two weeks after the plaster was applied and also 
 that the modern lime is not the same as the lime used thirty years 
 ago, either in the manner in which it is handled or in the manner 
 in which it sets and dries. It is particularly interesting to note in 
 these observations, more clearly in the plotted curves, the phe- 
 nomenon of resonance as shown by the maxima, and the effect of 
 the increased thickness produced by the skim coat in increasing the 
 rigidity of the wall, decreasing its absorbing power, and shifting the 
 resonance. 
 
 The most iirmlj^ established traditions of both instrumental and 
 architectural acoustics relate to the use of wood and excite the 
 liveliest interest in the effect of wood sheathing as an interior sur- 
 face for auditoriums; nor are these expectations disappointed when 
 the i)lK'nonK'non is submitted to exact measurement. It was not 
 easy to find satisfactory conditions for the experiment, for not 
 many rooms are now constructed in which plaster on studding, and 
 sufficiently thin, forms a very considerable factor. After long waiting 
 a room suitable in everj- respect, except location, became available. 
 Its floor, its whole wall, indeed, its ceiling was of pine sheath- 
 ing. The only other material entering into its construction was 
 glass in the two windows and in the door. Unfortunately, the room 
 was on a prominent street, and immediately adjacent was an all- 
 night lunch room. Accurate experiments were out of the question 
 while the lunch room was in use, and it was, therefore, bought out 
 and closed for a few nights. Even with the freedom from noise 
 thus secured, the experiments were not totally undisturbed. The 
 traffic past the building did not stop sufficiently to permit of any 
 observations until after two o'clock in the morning, and began again 
 by foiu". During the intervening two hours, it was possible to 
 snatch periods for observation, but even these periods were dis- 
 turbed through the curiosity of passers and the more legitimate 
 concern of the police. 
 
 Anticipating the phenomenon of resonance in wood in a more 
 marked degree than in any other material, new apparatus was 
 designed permitting of measurements at more frequent intervals 
 of pitch. The new apparatus was not available when the work
 
 :\n'SICAL PITCH ^,'((7 
 
 began and the coefficients for the wood were deterniiiicd ;il octave 
 intervals, with resuHs as follows: 
 
 Ci, .064; Co, .098; C,, .112; C*, .104; C., .081; Ce, .082; Ct, .U.S. 
 
 These results when plotted .^llowed clearly a very marked reso- 
 nance. The more elaborate apparatus was hastened to completion 
 and the coefficients of absorption determined for the intermediate 
 notes of E and G in each of the middle four octaves. The results of 
 both sets of experiments when plotted together give Curve 5 in 
 Fig. 1. The accuracy with which these fourteen jxiints fall on a 
 smooth curve drawn through them is all llial ((mid lie cxjx'cted in 
 view of the conditions under which the experiment was conducted 
 and the limited time available. Only one j)oint falls far from the 
 curve, that for middle C (C3, "250). The general trend of the curve. 
 however, is e.stablished beyond rea.sonable doubt. It is interesting 
 to note the \-erv great differenci's bet\\(<'ii this curve and tho.se 
 obtained lor solid walls, and even for plastered walls. It is espe- 
 cially interesting to note the great absorjjtion due to the resonance 
 between the natural vibration of the walls and the sound, and to 
 observe that this maximum i)<)int of resonance lies in the lower i)art, 
 although not in the lowest \n\r\, of the range of j)itcli tested. The 
 pitch of this resonance is determined by the nature of the wo(kI, its 
 thickness, and the distance apart of the stutlding on which it is 
 supported. The wood tested was North Carolina pine, five-eighths 
 of an inch in thickness and on studding fourteen inches apart. It 
 is, perhaps, not superfluous to add at this time that a denser wood 
 woulil have had a lower i)itch for nuixinunn resonance, other con- 
 ditions being alike; an increa.sed thickness would have raised the 
 |)it(li of llie resouaiice; while an iiierea>ed distance betwtHMi the 
 studding would have lowered it. I'inally it should be addetl that 
 the best acoustical condition both for music and for speaking would 
 have been with the nuiximum resonance an octave al)ove rather 
 than at middle C. 
 
 Even more interesting is the study of ceramic tih- made at the 
 ref|uest of Messrs. Cram, (Joodhue, and Ferguson 'Ihe iiiv«'sliga- 
 tion had for its first object the determination of the acoustical 
 value of the tile as employed in the grointnl arches of the Chapel of
 
 208 BLTILDING M.\TERIAL 
 
 tlic T'liitcd States Military Academy at West Point. The investi- 
 gation then widened its scope, and, through the skill and great 
 knowledge of ceramic processes of Mr. Raphael Guastavino, led to 
 really remarkable results in the way of improved acoustical effi- 
 ciency. The resulting construction has not only been approved by 
 architects as equal, if not better, in architectural appearance to 
 ordinary tile construction, but it is, so far as the writer knows, the 
 first finished structural surface of large acoustical efficiency. Its 
 random use does not, of course, guarantee good acoustical quality 
 in an auditorium, for that depends on the amount used and the 
 surface covered. 
 
 The first investigation was in regard to tile used at West Point, 
 with the following result : 
 
 Ci, .012; C2, .013; C3, .018; C4, M9; C„ .040; Ce, .048; C7, .053. 
 
 These are plotted in Curve 1, Fig. 2. The first endeavors to im- 
 prove the tile acoustically had very slight results, but such as they 
 were they were incorporated in the tile of the ceiling of the First 
 Baptist Church in Pittsburgh (Curve 2, Fig. 2). 
 
 Ci, .028; C2, .030; C3, .038; C4, .053; C5, .080; Ce, .102; C7, .114. 
 
 There was no expectation that the results of this would be more 
 than a very slight amelioration of the difficulties which were to be 
 expected in the church. In consequence of its use, the tile may be 
 distinguished for purposes of tabulation as Pittsburgh Tile. With- 
 out following the intermediate steps, it is sufficient to say that the 
 experiments were continued nearly two years longer and ultimately 
 led to a tile which for the conveniences of tabulation we will call 
 Acoustical Tile. The resulting absorbent power is far beyond what 
 was conceived to be possible at the beginning of the investigation, 
 and makes the construction in which this tile is incorporated unique 
 in acoustical value among rigid structures. The coefficients for this 
 construction are as follows: 
 
 Ci, .064; C2, .068; C3, .117; C4, .188; C„ .250; Ce, .258; C7, .223, 
 
 graphically shown in Curve 3, Fig. 2. It is not a panacea. There 
 is, on the other hand, no question but that properly used it will very 
 greatly ameliorate the acoustical difficulties when its employment
 
 MUSICAL PITCH 
 
 209 
 
 is practicable, and used in proper locations and amounts will render 
 the acoustics of many auditoriums excellent which would otherwise 
 be intolerable. It has over sixfold tlic ahsorbiiif,' [)ower of any exist- 
 ing masonry construction and oiu'-tliird tiic ahsorhing power of the 
 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 S 
 
 \ 
 
 
 
 
 / 
 
 
 \ 
 
 
 
 / 
 
 
 
 
 
 
 / 
 
 4 
 / 
 
 
 
 
 
 
 / 
 
 .X 
 
 f^ ^ 
 
 -\ 
 
 
 ^ 
 
 
 
 
 
 
 -^ 
 
 ^rr 
 
 :=:= 
 
 '2 
 
 
 -'' 
 
 
 — 
 
 ' 
 
 c, 
 
 c. 
 
 C, C, Cj c. 
 
 Fig. i. Absorbing power: 1, West Point tile; 2, Pitls- 
 
 l)iir(;li tile; 3, arotisticnl tile; \, best felt. 
 
 best known felt |)lott((l on tlie same diagram for comparison (Curve 
 4). It is a new factor ;il I lie dis])()sal of tlu' architect. 
 
 ClI.\lH.S .\N» AUDIKXCE 
 
 Efiually itM|)oil;mt witli the \\;ill ;m<l eeiling-surfaees of an 
 auditorium arc its conlcnls, cspcciidiy I lie scats and tlic audirnec. 
 
 In Impressing I la- coellii'ienls of al>sor|)tion for objects whieh are 
 themselves units ami which eamiol be hgured lus areius, the coefli-
 
 210 
 
 BOLDING :MATERIAL 
 
 cicnts clci)i'iul on iiic .system of measurement employed, Metric or 
 English. While the international or metric system has become 
 universal except in English speaking countries, and even in England 
 and America in many fields, it has not yet been adopted by the 
 
 10 
 
 
 
 
 
 
 
 9 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 7 
 
 
 
 
 
 
 
 6 
 
 
 
 
 
 
 
 5 
 
 
 
 /6- 
 
 
 
 
 
 
 
 4 
 
 / 
 
 X 
 
 
 
 
 
 3 
 
 /1 
 
 
 
 
 _^ 
 
 
 a 
 
 / 
 
 
 "M 
 
 
 s 
 
 \v, 
 
 
 -J 
 
 ■- \ 
 
 ^ 
 
 1 
 
 y ^^ 
 
 Z=^ 
 
 
 I , 
 
 
 -^ 
 
 c, 
 
 c. 
 
 c, 
 
 C,; 
 
 c, 
 
 c, c, 
 
 Fig. 3. Absorbing power: 1, bent wood chairs; 2, 3, 4, 
 and 5, various kinds of pew cushions as described in 
 text; 0, audience per person. 
 
 architectural profession and by the building trades, and therefore 
 these coefficients will be given in both systems. 
 
 Ash settees or chairs, such as are ordinarily to be foimd in a 
 college lecture-room, have exceedingly small absorbing powers. 
 Such furniture forms a very small factor in the acoustics of any 
 auditorium in which it is employed. The coeflBcients for ash chairs 
 are as follows (Curve 1, Fig. 3):
 
 MUSICAL PITCH 211 
 
 Metric 
 C„.014; C2, .014; Cj, .015; C4. .016; Cj, .017; C«. .019; C7. .021. 
 
 Knglitih 
 C, .15; C, .15; C3, .16; C^, .17; C,, .18; Ce, .20; C7, 23. 
 
 The coefficients for settees were also determined, hut differ so little 
 from those for chairs that this pajjer will not he hurdened with 
 them. When, however, the seats are upholstered, they immediately 
 become a considerable factor in the acoustics of an empty, or par- 
 tially empty, auditorium. Of course the chairs either upholstered 
 or unui)liolstered are not a factor in the acoustics of the auditorium 
 when occupied. The absorbing power of cushions depends in con- 
 siderable measure upon the nature of the covering and upon the 
 nature of the padding. Tlie cushions experinu-nted ui)on were such 
 SIS are employed in church pews, hut the coifiicients are expressed 
 in terms of the cushion which would cover a single seat. The co- 
 eflBcients are as follows: 
 
 Cushions of wiry vegetal)le fiber covered witli canvas and a thin 
 damask cloth (Curve '■2, Fig. .'5): 
 
 Metric 
 C,, .060; C2, .070; C3, .097; C4, .135; C,, .148; C,, .132; C7, .115. 
 
 English 
 Ci, .64; Cj, .75; C,, 1.04; C4, 1.45; Cs, 1.59; Ct, 1.42; C-, 1.24. 
 
 Cushions of long hair covered with canvas and with an outer 
 covering of plusii (Curve 15, Fig. .'5): 
 
 Metric 
 C .080; C2, .092; C3, .105; C4, .165; C,. .155; C,. .128; Cj, .085. 
 
 F.nglinh 
 C. .86; C5, .09; C,, 1.13; („ 1.77; C,, 1.67; C», 1.37; C7. .91. 
 
 Cushions of hair covered with canvas and an outer covering of 
 thin leatherette (Curve 4, Fig. 3): 
 
 Metric 
 C„.062; C», .105; Cj. .118; C,. .ISd; (\, .IIS; C,. .06H; C,. .040.
 
 '2U BUILDING MATERIAL 
 
 English 
 C„ .67; Co, 1.13; C,, 1.27; C4, 1.93; C^, 1.27; Cj, .73; C7, .43. 
 
 Elastic felt cushions of commerce, elastic cotton covered with 
 canvas and a short nap plush (Curve 5, Fig. 3) : 
 
 Metric 
 Ci, .092; Co, .155; C3, .175; C4, .190; Cs, .258; Ce, .182; C7, 120. 
 
 English 
 Ci, .99; C2, 1.66; C3, 1.88; C4, 2.04; d, 2.77; Ce, 1.95; C7, 1.29. 
 
 Of all the coefficients of aV)sorption, obviously the most diflScult 
 to determine are those for the audience itself. It would not at all 
 serve to experiment on single persons and to assume that when a 
 number are seated together, side by side, and in front of one an- 
 other, the absorbing power is the same. It is necessary to make the 
 experiment on a full audience, and to conduct such an experiment 
 recjuires the nearly perfect silence of several hundred persons, the 
 least noise on the part of one vitiating the observation. That the 
 experiment was ultimately successful beyond all expectation is due 
 to the remarkable silence maintained by a large Cambridge audi- 
 ence that volunteered itself for the purpose, not merely once, but 
 on four separate occasions. The coefficients of absorption thus de- 
 termined lie, with but a single exception, on a smooth curve (Curve 6, 
 Fig. 3). The single exception was occasioned by the sound of a 
 distant street car. Correcting this observation to the curve, the 
 coefficients for an audience per person are as follows : 
 
 Metric 
 Ci, .160; C2, .332; C3, .395; C4, .440; C5, .455; Ce, .460; C7, .460. 
 
 English 
 Ci, 1.72; C2, 3.56; C3, 4.25; C4, 4.72; Cs, 4.70; Ce, 4.95; C7, 4.95. 
 
 Fabrics 
 
 It is e\'ident from the above discussion that fabrics are high 
 absorbents of sound. How effective any particular fabric may be, 
 depends not merely on the texture of its surface and the material.
 
 MUSICAL PITCH 
 
 213 
 
 but upon the weave or felting throughout its body, and of course, 
 also upon its thickness. An illuminating study of this question 
 can be made by means of the curves in Fig. 4. In this figure are 
 plotted the coefficients of absorption for varying thicknesses of felt. 
 Curve 1 is the absorption curve for felt of on<'-lialf iiuh thickness. 
 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,^ 
 
 ^ 
 
 
 
 
 k 
 
 
 1^ 
 
 ^^ 
 
 
 
 // 
 
 
 f 
 
 
 
 V 
 
 / / 
 
 // 
 
 1 
 
 1 
 
 r 
 
 
 ^y 
 
 // 
 
 
 / 
 
 1 
 
 
 
 
 / 
 
 / 
 
 / 
 
 
 
 ^ 
 
 y 
 
 / 
 
 
 
 
 — - 
 
 -^ 
 
 ^ 
 
 
 
 
 c, 
 
 c. 
 
 c. 
 
 c. 
 
 c, 
 
 Kici. 4. Absorbing power of felt of varying thirkm-sji. from 
 oiii'-lmlf to llirce iiiclii-s. showing by exlni|M>lnlii)ii llie 
 nbsoriilion l>y lliiii fabrics of tbr ii|>|iir nxi^'i'r only. 
 
 Curve 2 of fell of one incli thickness, anil so on up to Curve (>, which 
 is for felt of three incht-s in tiiickness. It is interesting to contem- 
 plate what the result of the process would be were it continued to 
 greater thickness, or in the o|)|)osite direction to felt of less and less 
 thickness. It is incoii(<'iva])lc fliat felt should be ust-d more than 
 three inches in thickness and, therefore, extrapolation in lliis direc-
 
 i214 BllLDIXG ISLVTERIAL 
 
 tion is of academic interest only. On the other hand, felt with de- 
 creasing thickness corresponds more and more to ordinary fabrics. 
 If this process were carried to an extreme, it would show the eflfect 
 of cheesecloth or hunting as a factor in the acoustics of an audito- 
 rium. It is obvious tliat very thin fabrics absorb only the highest 
 notes and are negligible factors hi the range of either the speaking 
 voice or of music. On the other hand, it is evident that great thick- 
 ness of felt absorbs the lower register without increasing whatever 
 its absorption for the upper register. Sometimes it is desirable to 
 absorb the lower register, sometimes the upper register, but far more 
 often it is desirable to absorb the sounds from C3 to Ce, but espe- 
 cially in the octave between C4 and Cg. 
 
 The felt used in these experiments was of a durable nature and 
 largely composed of jute. Because wool felt and ordinary hair felt 
 are subject to rapid deterioration from moths, this jute felt was the 
 only one which could be recommended for the correction of audi- 
 toriums until an interested participator in these investigations de- 
 \el()ped an especially prepared hair felt, which is less expensive than 
 jute felt, but which is much more absorbent. Its absorption curve 
 is plotted in Fig. i. 
 
 Location 
 
 Such a discussion as this should not close without pointing out 
 the triple relation between pitch, location, and apparent power of 
 absorption. This is shown in Fig. 5. Curve 1 shows the true co- 
 eflBcient of absorption of an especially effective felt. Curve 2 is its 
 apparent absorption when placed in a position which is one of loud- 
 ness for the lower register and of relative silence for the upper 
 register. Curve 3 is the apparent coefficient of absorption of the 
 same felt when placed in a position in the room of maximum loud- 
 ness for all registers. It is evident from these three curves that in 
 one position a felt may lose thirtj^ per cent and over of its efficiency 
 in the most significant register, or may have its cfficiencj' nearly 
 doubled. These curves relate to the efficiency of the felt in its effect 
 on general reverberation. Its efficiency in the reduction of a dis- 
 cTete echo is dependent to an even greater degree on its location 
 than on pitch.
 
 MUSICAL PITCH 
 
 215 
 
 The above are the coefficients of absorption for most materials 
 usually occurring in auditorium construction, but there are certain 
 omissions which it is highly desirable to supply, particularly notice- 
 able among these is the absorption curve for glass and for old phister. 
 
 10 
 
 Fio. 5. Uoulilc <lo|>riiil<-n<c iif iiliwirlpiin! |ii>«rr ■•ii iJiloh 
 and on liK-ntiiin. sliouinK one of llir wmrifs of error 
 nliii'li iiiiist l>r K'uanli-tl n»;iiiii!it in tlir ilrtrnnination of 
 riK-iririfnls of uli!W>r|ilion ami in llic n»r of nlisoriiing 
 iiintcriaU.
 
 ^>1(5 BUILDING MATERIAL 
 
 It is necessary for such experiments that rooms practically free from 
 furniture should be available and that the walls and ceiling of the 
 room should be composed in a large me.asure of the material to be 
 testetl. The author would aj)preciate any opportunity to carry out 
 such experiments. The opportunity would ordinarily occur in the 
 construction of a new building or in the remodeling of Jin old one. 
 
 It may be not wholly out of place to point out another modern 
 acoustical difficulty and to seek opportunities for securing the neces- 
 sary data for its solution. Coincident with the increased use of 
 reenforced concrete construction and some other building forms 
 there has come increased complaint of the transmission of sound 
 from room to room, cither through the walls or through the floors. 
 Whether the present general complaint is due to new materials and 
 new methods of construction, or to a greater sensitiveness to un- 
 necessary noise, or whether it is due to greater sources of disturbance, 
 heavier traffic, heavier cars and wagons, elevators, and elevator 
 doors, where elevators were not used before, — whatever the cause 
 of the annoyance there is urgent need of its abatement in so far as 
 it is structurally possible. Moreover, several buildings have shown 
 that not infrequently elaborate precautions have resulted disas- 
 trously, sometimes fundamentally, sometimes through the oversight 
 of details which to casual consideration seem of minor importance. 
 Here, as in the acoustics of auditoriums, the conditions are so com- 
 plicated that only a systematic and accurately quantitative investi- 
 gation will yield safe conclusions. Some headway, perhaps half a 
 year's work, little more than a beginning, was made in this investi- 
 gation some years ago. Methods of measurements were developed 
 and some results were obtained. Within the past month the use of 
 a room in a new building, together with that of the room immedi- 
 ately below it, has been secured for the period of two years. Be- 
 tween these rooms the floor will be laid in reenforced concrete of two 
 thicknesses, five inches and ten inches, in hollow tile, in brick arch, 
 in mill construction, and with hung ceiling, and the transmission of 
 sound tested in each case. The upper surface of the floor will be 
 laid in tile, in hardwood, with and without sound-deadening lining, 
 and covered with linoleum and cork, and its noise to the tread 
 measured.
 
 MUSICAL PITCH 217 
 
 However, such experiments hut lay the foundation. What is 
 needed are tests of I lie walls and floors of rooms of various sizes, and 
 of the more varied construction which occurs in practice, in rooms 
 connecting with offsets and different floor levels, — the complicated 
 condition of actual building as against the sinii)lified conditions of 
 an orderly experiment. The one will give numerical coeflicicnts, 
 the other, if in sufficiently full measure, will give experience leading 
 to generalization which may be so formulated as to be of wide value. 
 What is therefore sought is the opportunity to exjieriment in rooms 
 of varied but accurately known construction, especially where the 
 insulaticm has been successful. I'nfortunately, with modern build- 
 ing materials acoustical difficulties of all sorts are very numerous.
 
 ARCHITECTUKAL ACOUSTICS' 
 
 Jjecause familiarity- with Ihe phenomena of sound has so far out- 
 stripped the adequate study of the jiroblenis involved, many of them 
 have been popularly shrouded in a wholly unnecessary mysterj'. 
 Of none, i)erhaps, is this more true than of architectural acoustics. 
 The conditions surrounding; the transmission of speech in an en- 
 closed auditorium are complicated, it is true, but are only such as 
 will yield an exact solution in the lifjht of adequate data. Tt is, in 
 other words, a rational engineering problem. 
 
 The problem of architectural acoustics is necessarily complex, 
 and each room presents main' coiidil ions which contribute to the 
 result in a greater or less degree. ac(t)rding to circumstances. To 
 take justly into account these varied conditions, the solution of the 
 problem should be quantitative, not merely qualitative; and to 
 reach its highest usefulness and the dignity of an engineering science 
 it should be such that its application can precede, not merely follow, 
 the construction of the building. 
 
 In order that hearing may be good in any awditoriiun it is neces- 
 sary that the .sound should be sufficiently loud, that the simulta- 
 neous components of a complex sound should maintain their jiroper 
 relative intensities, and that the successive sounds in rapidly moving 
 articulation, eitlu-r of si)et'cli or of nuisic, should be dear and distinct, 
 free from each other and from extraneous noises. These three are 
 the necessarj', as they are the entirely sufficient, conditions for good 
 hearing. Scientifically the proi)lem involves three factors: rever- 
 beration, interference, and resonance. As an engineering j)roblem 
 it involves the shape of the auditorium, its dimensions, and the 
 materials of which it is composed. 
 
 Sound, i>eiug ciiergA', once ])roduced in a confined space, will 
 continue until it is either traii-<niitted by the boun<lar>' walls or is 
 transformed into some other kind of i-nerg^', generally heal. This 
 process of decay is called al)sorption. Thus, in the lecture-rtK>m of 
 
 ' The Jouriiul uf the Franklin Inxlitutc, Januar}-, 1013.
 
 220 ARCIIITECTITRAL ACOUSTICS 
 
 Harvard rnivorsity, in which, and in behalf of which, tliis investi- 
 gation was begun, the rate of absorption was so small that a word 
 spoken in an ordinary tone of voice was audible for five and a half 
 seconds afterwards. During this time even a very deliberate speaker 
 would have uttered the twelve or fifteen succeeding syllables. Thus 
 the successive enunciations blended into a loud sound, through 
 which and above which it was necessary to hear and distinguish the 
 orderly progression of the speech. Across the room this could not 
 be done; even near the speaker it could be done only with an effort 
 wearisome in the extreme if long maintained. With an audience 
 filling the room the conditions were not so bad, but still not tolerable. 
 This may be regarded, if one so chooses, as a process of nniltiple re- 
 flection from walls, from ceiling, and from floor, first from one and 
 then another, losing a little at each reflection until ultimately in- 
 audible. This phenomenon will be called reverberation, including, 
 as a special case, the echo. It nuist be observed, however, that, in 
 general, reverberation results in a mass of soimd filling the whole 
 room and incapable of analysis into its distinct reflections. It is 
 thus more difficult to recognize and impossible to locate. The term 
 "echo" will be reserved for that particular case in which a short, 
 sharp sound is distinctly repeated by reflection, either once from a 
 single surface, or several times from two or more surfaces. In the 
 general case of reverberation we are concerned only with the rate of 
 decay of the sound. In the special case of the echo we are concerned 
 not merely wnth its intensity, but with the interval of time elapsing 
 between the initial sound and the moment it reaches the observer. 
 In the room mentioned as the occasion of this investigation no dis- 
 crete echo was distinctly perceptible, and the case will serve ex- 
 cellently as an illustration of the more general type of reverberation. 
 After preliminary gropings, first in the literature and then with 
 several optical devices for measuring the intensity of sound, all 
 established methods were abandoned. Instead, the rate of decay 
 was measured by measuring what was inversely proportional to it, 
 — the duration of audibility of the reverberation, or, as it will be 
 called here, the duration of audibility of the residual sound. These 
 experiments may be explained to advantage here, for they will give 
 more clearly than would abstract discussion an idea of the nature
 
 ARCniTFXTniAL ACOUSTICS 
 
 221 
 
 of reverberation. Broadly considered, there are two, and only two, 
 variables in a room, — shape (including size) and materials (includ- 
 ing furnishings). In designing an auditorium an architect can give 
 consideration to both; in r»'j)air work for liad acoustic conditions it 
 is generally impracticable to change the shape, and only variations 
 in materials and furnishings are allowable. This wiis, therefore, 
 the line of work in this cas<'. It was evident that, other things being 
 equal, the rate at which the reverlxTation would disappear was 
 proi)ortional to the rate at which the sound wa.s absorbed. The 
 first work, therefore, was to detennine the relative absorbing power 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 *h 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 «>«. 
 
 ►-> 
 
 t^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 *~- 
 
 
 -»-. 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10 
 
 9 
 
 8 
 7 
 6 
 
 S 
 4 
 3 
 2 
 1 
 
 "25 40 60 80 100 120 140 160 140 ZOO 220 240 Z&O 280 300 
 
 Length of cushions in meters 
 
 Fio. 1. Curve showing the relation of the duration of the residual 
 sound to thi- addiil absorbing material. 
 
 of various substances, ^^■ilh an organ pipe as a constant source of 
 soimd, and a suitable chronograi)h for recording, the duration of 
 audibility of a sound after the source had ceased in tiiis room when 
 empty was found to be o.G'-i seconds. All the cushions from tiie 
 seats in Sanders Theatre were then brought over and stored in the 
 lobby. On bringing into the Icctun-room a number of cushions, 
 having a total length of 8.-2 meters, the duration of audibility fell to 
 5.:53 seconds. Ou bringing in 17 meters the sound in the room after 
 the organ pipe ceiused wius audible for l)ut 4.94 stH-onds. Kvidently 
 the cushions were strong absorbents and ra|)idly improving the 
 room, at lea^st to the extent of diminishing the reverberation. The 
 result wa.s interesting and the process was contimied. Little by 
 little the cushions were brought into the riMjm, and each lime the
 
 222 
 
 ARCHITPXTURAL ACOUSTICS 
 
 duration of audibility was measured. When all the seats (436 in 
 number) were covered, the sound was audible for 2.03 seconds. 
 Then the aisles were covered, and then the platform. Still there 
 were more cusliioiis, - almost half as many more. These were 
 broufjhl into the room, a few at a time, as before, and draped on a 
 scafTolding that had been erected around the room, the duration of 
 the sound being recorded each time. Finally, when all the cushions 
 from a theatre seating nearly fifteen hundred persons were placed 
 in tlie room — covering the seats, the aisles, the platform, the rear 
 wall to the ceiling — tiie duration of audibility of the residual sound 
 
 •g 
 
 
 ■ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 V, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ' — , 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — 
 
 
 — 
 
 — 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 80 
 
 Walls 
 
 160 
 
 240 
 
 320 400 
 
 Cushions 
 
 480 
 
 560 
 
 Fig. 2. Curve 5 plotted as part of its corresponding rectangular 
 hj-perbola. The solid part was determined experimentally; 
 the displacement of this to the right measures the absorbing 
 power of the walls of the room. 
 
 was 1.14 seconds. This experiment, requiring, of course, several 
 nights' work, having been completed, all the cushions were removed 
 and the room was in readiness for the test of other absorbents. It 
 was evident that a standard of comparison had been established. 
 Curtains of chenille, 1.1 meters wide and 17 meters in total length, 
 were draped in the room. The duration of audibility was then 4.51 
 seconds. Turning to the data that had just been collected, it ap- 
 peared that this amount of chenille was equivalent to 30 meters of 
 Sanders Theatre cushions. Oriental rugs (Herez, Demirjik, and 
 Ilindoostanee) were tested in a similar manner, as were also cretonne 
 cloth, canvas, and hair felt. Similar experiments, but m a smaller
 
 ARCHITECTURAL ACOUSTICS 223 
 
 room, determined the absorbing power of a man and of a woman, 
 always by determining the number of running meters of Sanders 
 Theatre cushions that would produce the same effect. This process 
 of comparing two absorbents ])y actually substituting one for the 
 other is laborious, and it is given lu-re only to show the first steps 
 in the development of a method. Without going into details, it is 
 sufficient here to say that this method was so perfected as to give 
 not merely relative, but absolute, coefficients of absorption. 
 
 In this manner a number of coefficients of absorption were de- 
 termined for objects and materials which could be brought into 
 and removed from the room, for sounds having a pitch an octave 
 above middle C. In the following table the numerical values are 
 the absolute coefficients of the absorption: 
 
 Oil paintings, inclusive of frames 28 
 
 Carpel rugs 20 
 
 Oriental rugs, extra heavy 29 
 
 Cheesecloth 019 
 
 Cretonne <lotli 15 
 
 Shelia curtains 23 
 
 Hair felt, 2.5 cm. thick, 8 cm. from wall 78 
 
 Cork, i.3 cm. thick, loose on floor 16 
 
 Linoleum, loose on floor 12 
 
 When the objects are not extended surfaces, such as carpets or 
 
 rugs, but essentially spacial units, it is not easy to express the 
 
 absorption as an absolute coefficient. In the following table the 
 
 al)sori)tion of each object is expressed in terms of a square meter of 
 
 complete absorption: 
 
 Audience, per person 44 
 
 Isolated woman 54 
 
 Isohite<l man 48 
 
 Plain ash settees 039 
 
 I'lain ash settees, per single scat 0077 
 
 riain ash chairs, " hcnt w(mm1 " 0082 
 
 I pliolstercd sctlecs, hair and leather 1.10 
 
 1 pholstcreil si'tlecs, per single seat iJS 
 
 I'pholstcriil chairs similar in style SO 
 
 Hair cushions, per .seat 21 
 
 Klastic fell cushions, [)er scut 20 
 
 Of tvcu gnahr importance was tlie (ittermination of tlic ct)- 
 cfficient of ab.sori)fion of fl(M)rs, ceilings, and wall-surfa<vs. TIk-
 
 224 
 
 ARCHITECTURAL ACOUSTICS 
 
 accoinplishiiK'iil of this called for a very considerable extension of 
 the method adopted. If the reverberation in a room as changed 
 by the addition of absorbing material be plotted, the resulting 
 curve will be found to be a portion of an hyperbola with displaced 
 axes. An example of such a curve, as obtained in the lecture- 
 room of the Fogg Art Museum, in Cambridge, is plotted in the 
 diagram. Fig. 1. If now the origin of this curve be displaced so 
 that the axes of coordinates are the asymptotes of the rectangular 
 hjT)erbola, the displacement of the origin measures the initial ab- 
 
 10 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5;; ; \ 
 
 1 
 
 \ 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 "2 ft 
 
 
 
 
 .^ 
 
 s. 
 
 
 ^N, 
 
 
 
 
 
 
 
 
 
 1'.; i* \ 
 
 \ 
 
 \ 
 
 
 \ 
 
 s 
 
 
 '--, 
 
 
 
 
 
 
 _a 
 
 "?lr 
 
 \ 
 
 '\ 
 
 \ 
 
 *x^ 
 
 V 
 
 \. 
 
 
 
 "--- 
 
 .„. 
 
 
 
 
 a 4 
 
 .2 
 
 \^\ 
 
 \ 
 
 \ 
 
 \ 
 
 "■s 
 
 \ 
 
 
 ■--^ 
 
 
 
 
 "~" 
 
 ---^ 
 
 -12 
 
 £ 3 
 
 a 2 
 
 '> 
 
 ^,^ 
 
 Jv'S. 
 
 ^v 
 
 ^-.. 
 
 ■"8. 
 
 
 ^9- 
 
 
 ~10, 
 
 
 -IV 
 
 
 
 
 
 
 
 
 \^^ 
 
 -^-' 
 
 'r-'-s 
 
 
 -- 
 
 
 
 ""■ 
 
 
 
 - — 
 
 — 
 
 ; — 
 
 l"-- 
 
 IT.: 
 
 
 
 
 -'V,- 
 
 -%=-=i 
 
 
 ^--^=i 
 
 -"j:";^ 
 
 r.^V 
 
 r.-»r 
 
 fSi- 
 
 rC-i>^ 
 
 :-i-z4: 
 
 -z=iz' 
 
 10 20 30 40 SO 60 70 80 90 100 110 120 130 140 IGO 
 120 leO 240 300 360 420 
 540 720 900 1080 1360 
 
 Total absorbing material 
 
 Fig. 3. The curves of Figs. 8 and 9 entered as parts of their corre- 
 sponding rectangular hj-perbolas. Three scales are employed for 
 the volumes,, by groups 1-7, 8-11, and 12. 
 
 sorbing power of the room, its floors, walls, and ceilings. Such 
 experiments were carried out in a large number of rooms in which 
 the diflFerent component materials entered in very different degrees, 
 and an elimination between these different experiments gave the 
 following coefficient of absorption for different materials: 
 
 Open window 1.000 
 
 Wood sheathing (hard pine) 061 
 
 Plaster on wood lath 034 
 
 Plaster on wire lath 033 
 
 Glass, single thickness 027 
 
 Plaster on tile 025 
 
 Brick set in Portland cement 025
 
 ARCIIITECTI'RAL ACOUSTICS 
 
 225 
 
 If the experiments in these rooms are plotted in a single dia- 
 gram, the result is a family of hyperbolae showing a very interesting 
 relationship to the volumes of the rooms. Indeed, if from these 
 hj'perholas the parameter, which etjuals the product of the co- 
 ordinates, be deternn'ned, it will be found to be linearly j)ropor- 
 tional to the volume of the room. These results are plotted in 
 Fig. 4, showing how strict the proportionality is even over a very 
 great range in vohinic. We have thus at hand a ready method of 
 
 u 
 
 ISO - 
 
 •S 100 
 
 
 
 
 
 
 
 
 
 
 .<L 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 °u 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 MM 
 
 lOMo 
 
 12»00 
 
 
 
 
 
 1 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 1200 
 
 1800 
 
 2400 
 
 30C0 
 
 3600 
 
 4300 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 a 
 
 I : 
 
 
 
 1 
 
 
 
 I 
 
 600 800 lOOO 
 
 Volumes of rooms 
 
 IMO 
 
 Fig. 4. The parameter, k, plolled against the volumes of the 
 rooms, showing the two proportional. 
 
 calculating the reverberation for any room, its volume and the 
 materials of which it is composed being known. 
 
 The first five years of tlie investigation were devoted to violin 
 C, the C an octave above middle C, having a vibration frequency 
 of 512 vibrations i)er .second. This i)iteli was cho.sen becau.se, in 
 the art of telephony, it was regarded at liiat lime as the character- 
 istic pitch determining the conditions of articulate speech. The 
 planning of Syni|)h(my Hall in Hoston forced an extension of this 
 investigation to notes over tlie whole range of tlie musical .scale, 
 three octaves below and three octaves above violin ('. 
 
 In the verv- nature of the problem, the most important dalinn 
 is the alisorplion coeHicienl of an audience, and the determination 
 of thi> was tlie first task undtTtak.ii. \\\ nuaii- of a Ifctun- on
 
 i^2G ARCHITECTOiAL ACOUSTICS 
 
 one of llie recent de\elopments of physics, wireless telegraphy, an 
 audience was thus drawn together and at the end of the lecture 
 requested to remain for the experiment. In this attempt the effort 
 was made to determine Die coefficients for the five octaves from 
 C2I28 to CV2048, including notes E and G in each octave. For 
 several reasons the experiment was not a success. A threatening 
 thunderstorm made the audience a small one, and the sultriness of 
 the atmosphere made open windows necessary, while the attempt 
 to cover so many notes, thirteen in all, prolonged the experiment 
 beyond the endurance of the audience. While tliis experiment 
 failed, another the following summer was more successful. In the 
 year that had elapsed the necessity of carrj-ing the investigation 
 further than the limits intended became evident, and now the ex- 
 periment was carried from Ci64 to C7409G, but included only the 
 C notes, seven notes in all. Moreover, bearing in mind the experi- 
 ences of the previous summer, it was recognized that even seven 
 notes would come dangerously near overtaxing the patience of the 
 audience. Inasmuch as the coefficient of absorption for C4512 had 
 already been determined six years before, in the investigations 
 mentioned, the coefficient for this note was not redetermined. The 
 experiment was therefore carried out for the lower three and the 
 upper three notes of the seven. The audience, on the night of this 
 experiment, was much larger than that which came the previous 
 summer, the night was a more comfortable one, and it was possible 
 to close the windows during the experiment. The conditions were 
 thus fairly satisfactory. In order to get as much data as possible, and 
 in as short a time, there were nine observers stationed at different 
 points in the room. These observers, whose kindness and skill it is 
 a pleasure to acknowledge, had prepared themselves, by previous 
 practice, for this one experiment. The results of the experiment 
 are shown on the lower cur^'e in Fig. 5. This curve gives the co- 
 efficient of absorption per person. It is to be observed that one of 
 the points falls clearly off the smooth curve drawn tlirough the other 
 points.' The observations on which this point is based were, how- 
 ever, much disturbed by a street car passing not far from the build- 
 ing, and the departure of this observation from the curve does not 
 
 ' This point, evidently on the ordinate Cs, is omitted in the original cut. — Editor.
 
 ARCHITECTIRAL ACOUSTICS 
 
 227 
 
 inilicate a real departure in the coefficient, nor should it cast much 
 doubt on the rest of the work, in view of the circumstances under 
 which it was secured. Counteracting the, perhaps, bad impression 
 
 .0 
 
 
 
 
 -^ 
 
 
 
 .9 
 
 
 / 
 
 r 
 
 
 
 
 .U 
 
 / 
 
 / 
 
 
 
 
 
 .7 
 
 / 
 
 
 
 
 
 
 .6 
 
 / 
 
 
 
 
 
 
 .5 
 
 / 
 
 
 
 
 
 
 
 ^ 
 
 
 
 .4 
 
 / 
 
 /' 
 
 
 
 
 
 .3 
 
 / 
 
 
 
 
 
 
 .2 
 
 / 
 
 
 
 
 
 
 .1 
 
 
 
 
 
 
 
 c, 
 
 c. 
 
 c, 
 
 c. 
 
 c. 
 
 c, 
 
 Flii- J- 1 '»-■ uljsorbiiit; powrr of an uuiiieiicv fur iliircriiil 
 notes. Till' lower curve repre«Mits tlie iibsorliinK power 
 of uii audience per person. Tlie upper curve represents 
 llie absorbing power of an audience per sipinre meter 
 OS ordinarily sealed. The vertical ordinates arc ex- 
 pre.s-sed in terms of total absorption by a square meter 
 of surface. I'or the upper curve tlie ordinales ore thus 
 the onliiuiry cwllicieiits of absorption. The several 
 notes ore at octave intervals as follows: ('ilU. CM<8, 
 C, (middle C) i5«. ('.51i, (\\VH.\. C.itm. Cj+OUO. 
 
 wliich thi.s point may K've, it i.s a coii.sidtralile .sali.sfaetion to note 
 how accurately the |)oinl for C45H, determined .sL\ years U-fore by 
 a dilTereiit set of observers, falls on the smooth curve through the
 
 -228 ARCHITECTURAL ACOUSTICS 
 
 remaining points. In the audience on which these observations 
 wore taken there were 77 women and 105 men. The courtesy of 
 the audience in remaining for the experiment and the really re- 
 markable silence which they maintained are gratefully acknowl- 
 edged. 
 
 The next experiment was on the determination of the absorp- 
 tion of sound by wood sheathing. It is not an easy matter to find 
 conditions suitable for this experiment. The room in which the 
 absorption by wood sheathing was determined in the earlier ex- 
 |)eriments was not available for these. It was available then only 
 because the building was new and empty. When these more elabo- 
 rate experiments were under way the room became occupied, and 
 in a manner that did not admit of its being cleared. Quite a little 
 searching in the neighborhood of Boston failed to discover an en- 
 tirely suitable room. The best one available adjoined a night 
 lunch room. The night lunch was bought out for a couple of 
 nights, and the experiment was tried. The work of both nights 
 was much disturbed. The traffic past the building did not stop 
 until nearly two o'clock, and began again at four. The interest of 
 those passing on foot throughout the night, and the necessity of 
 repeated explanations to the police, greatly interfered with the 
 work. This detailed statement of the conditions under which the 
 experiment was tried is made by way of explanation of the irregu- 
 larity of the observations recorded on the curve, and of the failure 
 to carry this particular line of work further. The first night seven 
 points were obtained for the seven notes Ci64 to C74096. The re- 
 duction of these results on the following day showed variations 
 indicative of maxima and minima, which, to be accurately located, 
 would require the determination of intermediate points. In the 
 experiment the following night points were determined for the E 
 and G notes in each octave between Col28 and C62048. Other 
 points would have been determined, but time did not permit. It 
 is obvious that the intermediate points in the lower and in the 
 higher octave were desirable, but no pipes were to be had on such 
 short notice for this part of the range, and in their absence the data 
 could not be obtained. In the diagram. Fig. 6, the points lying on 
 the vertical lines were determined the first night. The points lying
 
 ARCHITECTURAL ACOUSTICS 
 
 229 
 
 between the vertical lines were determined the second night. The 
 accuracy with which these points fall on a smooth curve is, perhaps, 
 
 .12 
 
 .U 
 
 .10 
 .09 
 .08 
 .07 
 .06 
 .05 
 .04 
 .03 
 .02 
 .01 
 
 > 
 
 c. 
 
 c. 
 
 c. 
 
 c. 
 
 c, 
 
 Fig. (i. The absorbing powrr of wood sheathing, two centi- 
 meters thick, North Carolina pine. The ob.servations 
 were made under very unsuitable eiinilitions. The 
 abiiorplioii is here due almost wholly to yieliiing of the 
 sheathing as a wholi', the surface bi'ing shellacked, 
 smooth, and non-porous. The curve shows one point 
 of resonance within the range tested, anil the prob- 
 ability of anoth<T point of resonance alK>V4>. It is not 
 possible now lo learn as much in regard to the framing 
 anil arrangement of the studding in thi' particular room 
 tested us is desirable. (> (middle (') iM.
 
 O30 ARCHITECTURAL ACOUSTICS 
 
 all that could be expected in view of the difficulty under which the 
 observations were conducted and the linuted time available. One 
 point in particular falls far off from this curve, the point for C3256, 
 by an amount which is, to say the least, serious, and which can be 
 justified only by tlie conditions xmder which the work was done. 
 The general trend of the curve seems, however, established beyond 
 reasonable doubt. It is interesting to note that there is one point 
 of maximum absorption, which is due to resonance between the 
 walls and the sound, and that this point of maximum absorption 
 lies in the lower part, though not in the lowest part, of the range of 
 pitch tested. It would have been interesting to determine, had the 
 time and facilities permitted, the shape of the curve beyond C74096, 
 and to see if it rises indefinitely, or shows, as is far more likely, a 
 succession of maxima. 
 
 The experiment was then directed to the determination of the 
 absorption of sound by cushions, and for this purpose return was 
 made to the constant-temperature room. Working in the manner 
 indicated in the earlier papers for substances which could be carried 
 in and out of a room, the curves represented in Fig. 7 were obtained. 
 Curve 1 shows the absorption coefficient for the Sanders Theatre 
 cushions, with which the whole investigation was begun ten years 
 ago. These cushions were of a particularly^ open grade of packing, 
 a sort of wiry grass or vegetable fiber. They were covered with 
 canvas ticking, and that, in turn, with a very thin cloth covering. 
 Curve 2 is for cushions borrowed from the Phillips Brooks House. 
 They were of a high grade, filled with long, curly hair, and covered 
 with canvas ticking, which was, in turn, covered by a long nap 
 plush. Curve 3 is for the cushions of Appleton Chapel, hair covered 
 with a leatherette, and showing a sharper maximum and a more 
 rapid diminution in absorption for the higher frequencies, as would 
 be expected under such conditions. Curve 4 is probably the most 
 interesting, because for more standard commercial conditions ordi- 
 narily used in churches. It is to be observed that all four curves 
 fall off for the higher frequencies, all show a maximum located 
 within an octave, and three of the curves show a curious hump in 
 the second octave. This break in the curve is a genuine phenomenon, 
 as it was tested time after time. It is perhaps due to a secondary
 
 ARCHITECTLTRAL ACOUSTICS 
 
 231 
 
 resonance, and it is to be observed that it is the more pronounced in 
 those curves that have the sharper resonance in their principal 
 maxima. 
 
 1.0 
 
 .9 
 
 .6 
 
 .3 
 
 
 
 
 
 
 
 
 
 
 A 
 
 \ 
 
 
 
 
 //' 
 
 f 
 
 \ 
 
 
 
 ^ 
 
 •f 
 
 ^ 
 
 \ 
 
 \ 
 
 / 
 
 
 // 
 
 \ 
 
 \ 
 
 \\ 
 
 / ^ 
 
 ■* 
 
 V 
 
 \ 
 
 
 \ 
 
 ^ 
 
 7 
 
 
 
 
 \ 
 
 ^ 
 
 / 
 
 
 
 
 \ 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 c, 
 
 c. 
 
 c. 
 
 c. 
 
 c. 
 
 c, 
 
 FiQ. 7. The absorbing power of cushions. Curve 1 is 
 for "Sanders Theatre" cushions of wiry vegetable 
 6ber, covered with canvas ticking and a thin cloth. 
 Curve i is for "Brooks House" cushions of long hair, 
 covered with the same kind of ticking and plush. 
 Curve 3 is for ".\ppleton Chapel" cushions of hair, 
 covered with ticking and a thin liallnTctle. Curve 4 
 is for the elastic felt cushions of rinniiiiTce. of clastic 
 cotton, covered with ticking and short nap plush. The 
 absorbing power is per sipiare meter of surface. 
 Ci (middle C) tbO. 
 
 In both articuhile speccli and in music the source of soimd is 
 raj)i(IIy and. in fjcncral. abriii)lly cliaiiijint; in pitch, quality, and 
 loudne.**-'^. In niii.sic one i)itch is held duriny the leiiglh of a note.
 
 232 ARCHITECTUKAL ACOUSTICS 
 
 In articulate speech the unit or element of constancy is the syllable. 
 Indeed, in speech it is even less than the length of a syllable, for 
 the open vowel sound which forms the body of a syllable usually 
 has a consonantal opening and closing. During the constancy of 
 an element, either of music or of speech, a train of sound-waves 
 spreads spherically froTU the source, just as a train of circular 
 waves spreads outward from a rocking boat on the surface of still 
 water. Different portions of this train of spherical waves strike 
 different surfaces of the auditorium and are reflected. After such 
 reflection they begin to cross each other's paths. If their paths 
 are so differejit in length that one train of waves has entirely passed 
 before the other arrives at a particular point, the only phenomenon 
 at that point is prolongation of the sound. If the space between 
 the two trains of waves be sufficiently great, the effect will be that 
 of an echo. If there be a number of such trains of waves thus widely 
 spaced, the effect will be that of multiple echoes. On the other 
 hand, if two trains of waves have traveled so nearly equal paths 
 that they overlap, thej^ will, dependent on the difference in length 
 of the paths which they had traveled, either reenforce or mutually 
 destroy each other. Just as two equal trains of water-waves cross- 
 ing each other may entirely neutralize each other if the crest of one 
 and the trough of the other arrive together, so two sounds, coming 
 from the same source, in crossing each other may produce silence. 
 This phenomenon is called interference, and is a common phenom- 
 enon in all types of wave-motion. Of course, this phenomenon has 
 its complement. If the two trains of water-waves so cross that the 
 crest of one coincides with the crest of the other and trough with 
 trough, the effects will be added together. If the two sound-waves 
 be similarly retarded, the one on the other, their effects will also 
 be added. If the two trains of waves be equal in intensity, the 
 combined intensity will be quadruple that of either of the trains 
 separately, as above explained, or zero, depending on their relative 
 retardation. The effect of this phenomenon is to produce regions 
 in an auditorium of loudness and regions of comparative or even 
 complete silence. It is a partial explanation of the so-called deaf 
 regions in an auditorium.
 
 ARCHITECTURAL ACOUSTICS 
 
 233 
 
 It is not difficult to observe this phenomenon directly. It is 
 difficult, however, to measure and record the phenomenon in such 
 a manner as to permit of an accurate chart of the result. Without 
 going into the details of the method employed, the result of these 
 
 ^--^^^^ ^Z^V_^ 
 
 FlO. H. DLslrihuliim of iiili-ii.sily on the head level ill a room 
 with a barrel-shiipoil ceiling, with center of curvature on the 
 floor level. 
 
 measurements for a room very similar lo llu- ( ougregatioual ( luircli 
 in Naugatuck, Connecticut, is shown in the accompanying eliart. 
 The room exixTiniented in was a siinj)le, rectangular room with 
 plain side walls and ends and with a barrel or cylindrical ceiling. 
 The result is clearly repre.senled in Fig. 8, in which the intensity
 
 234 
 
 ARCHITECTniAL ACOUSTICS 
 
 of tlu- sound has l)eon indicated by contour linos in the manner 
 eini)loyed in the drawing of tlie geodetic survey maps. The phenom- 
 enon indicated in these diagrams was not ephemeral, hut was con- 
 stant so long as the source of sound continued, and repeated itself 
 with almost perfect accuracy day after day. Nor was the phenom- 
 
 Fio. 9 
 
 Fig. 11 
 
 Fig. 10 
 
 Fig. 1^ 
 
 enon one which could be observed merely instrumentally. To an 
 observer moving about in the room it was quite as striking a j)henom- 
 enon as the diagrams suggest. At the points in the room indicated 
 as high ma-xima of intensity in the diagram the sound was so loud 
 as to be disagreeable, at other points so low as to be scarcely audible. 
 It should be added that this distribution of intensity is with the 
 source of sound at the center of the room. Had the source of sound 
 been at one end and on the axis of the cylindrical ceiling, the dis-
 
 ARCHITEC TIRAL ACOUSTICS 
 
 235 
 
 tribution of intensity would still have been bilaterally symmetrical, 
 but not symmetrical about the transverse axis. 
 
 When a source of sound is maintained constant for a sufficiently 
 long time — a few seconds will ordinarily suffice the sound l)ecomes 
 steady at everj' point in the room, 'i'lie distribution of the intensity 
 
 Kk:. IM 
 
 Fig. 15 
 
 I'u,. U 
 
 Vu.. Hi 
 
 of sovmd iiiidii- llicse conditions is called the interference system, 
 for that ])arlicular ncttc, of the room or space in ciuestion. If tlic 
 source of sound is suddenly stojjped, it re((uires some time fur llic 
 sound in the room to be ab.sorbeil. This prolongation of sound after 
 the source has ceased is calle<l reverberation. If the source of sound, 
 instead of being nuiinlained, is short and sharp, it travels as a ilis- 
 crete wave or grou]) of waves about the room, reflected from wall to
 
 236 ARCHITECTURAL ACOUSTICS 
 
 wall, jjioducing echoes. In the Greek theatre there was ordinarily 
 but one echo, "doubling the case ending," while in the modern 
 auditorium there are many, generally arriving at a less interval of 
 time after the direct sound and therefore less distinguishable, but 
 stronger and therefore more disturbing. 
 
 The formation and the j)ropagation of echoes may be admirably 
 studied by an adaptation of the so-called schlieren-Methode device 
 for photographing air disturbances. It is sufficient here to say that 
 the adaptation of this method to the problem in hand consists in 
 the construction of a model of the auditorium to be studied to 
 proper scale, and investigating the propagation through it of a 
 proportionally scaled sound-wave. To examine the formation of 
 echoes in a vertical section, the sides of a model are taken off and, 
 as the .sound is passing through it, it is illuminated instantaneously 
 by the light from a very fine and somewhat distant electric spark. 
 In the preceding illustrations, reduced from the photographs, 
 the enframing silhouettes are shadows cast by the model, and all 
 within are direct photographs of the actual soimd-wave and its 
 echoes. The four photographs show the sound and its echoes at 
 different stages in their propagation through the room, the particu- 
 lar auditorium under investigation being the New Theatre in New 
 York. It is not difficult to identify the master wave and the vari- 
 ous echoes which it generates, nor, knowing the velocity of sound, 
 to compute the interval at which the echo is heard. 
 
 To show the generation of echoes and their propagation in a 
 horizontal plane, the ceiling and floor of the model are removed and 
 the photograph taken in a vertical direction. The photographs 
 shown in Figs. 13 to 16 show the echoes produced in the horizontal 
 plane passing through the marble parapet in front of the box. 
 
 While these several factors, reverberation, interference, and 
 echo, in an auditorium at all complicated are themselves compli- 
 cated, nevertheless they are capable of an exact solution, or, at 
 least, of a solution as accurate as are the architect's plans in actual 
 construction. And it is entirely possible to calculate in advance of 
 construction whether or not an auditorium will be good, and, if not, 
 to determine the factors contributing to its poor acoustics and a 
 method for their correction.
 
 10 
 
 THE INSULATION OF SOUND ^ 
 
 1 HE insulation of sound as an unsolved prohk-m in architectural 
 acoustics was first brought to the writer's attention by the New 
 England Conservatory of Music, immediately after its completion 
 in 1904, and almost simultaneously in connection with a private 
 house which had just been c()nii)leted in New York. A few years 
 later it was renewed by the Institute of ^Musical Art in New York. 
 In the construction of all three buildings it had been regarded as 
 particularly important that communication of sound from room to 
 room should be avoided, and methods to that end had been em- 
 ployed which were in every way reasonable. The results showed 
 that in this i)hase of architectural acoustics also there had not been 
 a sufficiently searching and practical investigation and that there 
 were no experimental data on which an architect could rely. As 
 these buildings were the oc-c-asion for beginning this investigation, 
 and were both instructive and suggestive, they are, with the con- 
 sent of the architects, discussed here at some length. 
 
 The special method of construction employed in the New England 
 Conservatory* of Music was suggested to the architects by the Trus- 
 tees of the Conservators'. The floor of each room was of semi-fire- 
 proof construction, cement between iron girtlers, on this a layer of 
 plank, on tliis j)apcr lining, and on top of this a floor of hard pine. 
 Between each room for violin, piano, or vocal lessons was a com- 
 ])()und wall, constructed of two i)artitions with an unobstructed air 
 space l)et\veen tiieui. Each partition was of two-inch plaster block 
 .set u|)right, with the finishing plaster applied directly to the block. 
 The walls surrounding tlic organ rooms were of tluce such ])artifions 
 separated by two-inch air spaces. In eacli air space was a con- 
 tinuous layer of deadening cloth. The scheme was carried out con- 
 sistently and witli full regard to details, yet lessons conducted in 
 adjacent rooms were (lislinl)ing In cacli ollu-r. 
 
 ' Till- UriiklmililiT, vul. xxiv, no. i, Fcbruury, 1015. 
 137
 
 238 THE INSULATION OF SOUND 
 
 It is always easier to explain why a method does not work than 
 to know in advance whether it will or will not. It is especially easy 
 to explain why it docs not work when not under the immediate neces- 
 sity of correcting it or of supplying a better. This lighter role of the 
 irresponsible critic was alone invited in the case of the New England 
 Conservatorj' of ^lusic, nor will more be ventured at the present 
 moment. 
 
 There is no question whatever that the fundamental considera- 
 tion on which the device hinged was a soimd one. Any discontinuity 
 diminishes the transmission of sovuid; and the transition from 
 masonrj' to air is a discontinuity of an extreme degree. Two solid 
 masonrj' walls entirely separated by an air space furnish a vastly 
 better sound insulation than either wall alone. On the other hand, 
 the problem takes on new aspects if a masonry wall be replaced by 
 a series of screen walls, each light and flexible, even though they 
 aggregate in massiveness the solid wall which they replace. More- 
 over, such screen walls can rarely be regarded as entirely insulated 
 from each other. Granting that accidental commimication has 
 nowhere been established, through, for example, the extrusion of 
 plaster, the walls are of necessity in communication at the floor, at 
 the ceiling, at the sides, or at the door jambs; and the connection at 
 the floor, at least, is almost certain to be good. Further, and of ex- 
 treme importance, given any connection at all, the thinness of the 
 screen walls renders them like drumheads and capable of large 
 response to small excitation. 
 
 It may seem a remote parallel, but assimie for discussion two 
 buildings a quarter of a mile apart. With the windows closed, no 
 ordinary sound in one building could be heard in the other. If, 
 however, the buildings were connected by a single metal wire 
 fastened to the centers of window panes, it would be possible not 
 merely to hear from within one building to within the other, but 
 with care to talk. On the other hand, had the wires been connected 
 to the hea\'j' masonry walls of the two buildings, such communica- 
 tion wovdd have been impossible. This hj-pothetical case, though 
 extreme, indeed perhaps the better because of its exaggeration, will 
 serve to analyze the problem. Here, as in everj' case, the transmis- 
 sion of sound involves three steps, — the taking up of the vibration.
 
 THE INSITATION OF SOT'XD 239 
 
 the function of the nearer window pane, its transmission by the wire, 
 and its coniniunication to the air of the receiving room by the remote 
 window. The three functions may be combined into one wlien a 
 solid wall separates the two rooms, the taking up, transmitting;, and 
 emitting of tlie sound being scarcely separable processes. On the 
 other hand, they are often clearly separable, as in the case of nndtiple 
 screen walls. 
 
 In the case of a solid masonrj' wall, the transmission from surface 
 to surface is almost perfect; but because of the great mass and 
 rigidity of tlie wall, it takes uj) but little of the vibration of the inci- 
 dent sound. It is entirely possible to express by a not verj' compli- 
 cated analytical e(|uation the amoimt of soimd which a wall of 
 simple dimensions will take up and transmit in terms of the mass 
 of the wall, its elasticity, and its viscosity, and the frequency of 
 vibration of the sound. But such an equation, while of possible 
 interest to physicists as an exercise, is of no interest whatever to 
 architects because of the difficulty of detennining the necessary 
 coefficients. 
 
 In the case of multiple screen walls, the conununication from 
 wall to wall, through the intermediate air space or around the edges, 
 is poor compared with the face to face connuunication of a solid 
 wall. But the vibration of the screen wall exposed to the sound, the 
 initial stej) in the process of transmission, is greatly enhanced by its 
 light and flexible character. Similarly its counterpart, the .screen 
 wall, which by its vibration connnunicates the sound to the receiv- 
 ing room, is light, flexible, and responsive to relatively small forces. 
 That this responsiveness of tin- walls compensates or more than 
 compensates for the poor communication between them, is the 
 probable explanation of the transmission betwetii tlu- rooms in the 
 New England Conservatory. 
 
 The Institute of Musical Art in New York presented interesting 
 variations of the problem. Here al.so the rooms on the second and 
 third floors were intended for private instruction and were designed 
 to be sound proof from each other, from the corridor, and from the 
 rooms above and below. The walls sejjarating the rooms from the 
 corridors were double, having connection only at the door jambs 
 and at the floor. The screen wall lu-xt llie corridor was of terra
 
 240 
 
 THE INSULATION OF SOLTND 
 
 cotta block, fiiiislied on tlie corridor side with plaster applied directly 
 to the terra cotta. The wall next the room was of gj-psum block, 
 plastered and finished in burlap. In the air space between the two 
 walls, deadening sheet was hung. The walls separating the rooms 
 were of gA'psum block and finished in hard plaster and burlap. As 
 siiown on the diagram (Fig. 1), these walls were cellular, one 
 
 SECTION TKROCOBBIDOli 
 PA(5TlTION WALL 
 
 Fig. 1. Details of Construction, Institute of Musical Art, 
 New York, N. Y. 
 
 of these cells being entirely enclosed in gypsum block, the others 
 being closets opening the one to one room, the other to the other. 
 The closets were lined with wood sheathing which was separated 
 from the enclosing wall by a narrow space in which deadening sheet 
 was himg in double thickness with overlapping joints. In the en- 
 tirely enclosed cell, deadening sheet was also hung in double thick- 
 
 ness.
 
 THE INSULATION OF SOUND 241 
 
 It is not difficult to see, at least after the fact, why the deadening 
 sheet in such positions was entirely without effect. The transverse 
 masonry webs afforded a direct transmission from side to side of the 
 compound wall that entirely overwhelmed the transmission through 
 the air spaces. Had there been no necessity of closets, and therefore, 
 no necessity of transverse web and had the two screen walls been 
 truly insulated the one from the other, not merely over their area, 
 but at the floor, at the ceiling, and at the edges, the insulation would 
 have been much more nearly perfect. 
 
 The means which were taken to secure insulation at the base of 
 the screen walls and to prevent the transmission of sound from floor 
 to floor are exceedingly interesting. The floor construction con- 
 sisted in hollow terra cotta tile arches, on top of this cinder concrete, 
 on this sawdust mortar, and on the top of this cork flooring. Below 
 the reenforced concrete arches were hung ceilings of plaster on wire 
 lath. This hung ceiling was supported by crossed angle bars which 
 were themselves supported by the I b«>ams which supported the 
 hollow terra cotta tile arches. In the air spaces between the tile 
 arches and the hung ceilings, and resting on the latter, was deaden- 
 ing sheet. This compound floor of cork, sawdust mortar, cinder 
 concrete, terra cotta tile, air space, and lumg ( ciliiig, with deadening 
 sheet in the air spaces, has the air of finality, but was not successful 
 in securing the desired insulation. 
 
 It is interesting to note also that the screen walls were separated 
 from the floor arches on which they rested below and on which they 
 abutted above by deadening sheet. It is possible that this afforded 
 some insulation at the top of the wall, for the arch was not sustained 
 by the wall, and the pressure at that point not great. At the bottom, 
 however, it is improbable tiial the deadening sheet carried under the 
 base offered an insulation of practical value. Under the weight of 
 the wall it was probably compressed into a compact mass, whose 
 rigidity was still furtlier increased by the percolation through it of 
 the cement from the surroinidiiig concrete- 
 Finally, after the completion of the building, Mr. Damrosch, the 
 director, had tried the cxpfriiiu-nt of covering tlie walls of one of the 
 rooms to a depth of two inches with slandanl hair felt, with some, 
 but almost negligible, effect on tlie transmission of sound.
 
 242 THE INSriATIOX OF SOUND 
 
 Deadoninj,' slu'ct has been mentioned frequently. All indication 
 of the special kind employed has been purposely omitted, for the 
 discussion is concerned with the larger question of the manner of its 
 use and not with the relative merits of the different makes. 
 
 The house in New York presented a problem even more interest- 
 ing. It was practically a double house, one of the most imperative 
 conditions of the building being the exclusion of sounds in the main 
 part of the hou.se from the part to the left of a great partition wall. 
 This wall of solid ma.sonrj' .supported only one beam of the main 
 house, was pierced by as few doors as possible — two — and by 
 no steam or water pipes. The rooms were heated by independent 
 fireplaces. The water pipes connected independently to the main. 
 It had been regarded as of particular importance to exclude .sounds 
 from the two bedrooms on the second floor. The ceilings of the 
 rooms below were, therefore, made of concrete arch; on top of this 
 was spread three inches of sand, and on top of this three inches of 
 lignolith blocks; on this was laid a hardwood floor; and finally, 
 when the room was occupied, this floor was covered by very heavy 
 and heavily padded carpets. From the complex floor thus con- 
 structed arose interior walls of plaster on wire lath on independent 
 studding, supported only at the top where they were held from the 
 masonr^' walls by iron brackets set in lignolith blocks. Each room 
 was, therefore, practically a room within a room, separated below 
 by three inches of sand and three inches of lignolith and on all sides 
 and above by an air space. Notwithstanding this, the shutting of a 
 door in any part of the main house could be heard, though faintly, 
 in either bedroom. In the rear bedroom, from which the best results 
 were expected, one could hear not merely the shutting of doors in 
 the main part of the house, but the working of the feed pump, the 
 raking of the furnace, and the coaling of the kitchen range. In the 
 basement of the main dwelling was the servants' dining room. Rap- 
 ping with the knuckles on the wall of this room produced in the bed- 
 room, two stories up and on the other side of the great partition wall, 
 a sound which, although hardly, as the architect expressed it, magni- 
 fied, yet of astonishing loudness and clearness. In this case, the 
 telephone-like nature of the process was even more clearly defined 
 than in the other cases, for the distances concerned were much
 
 THE INSULATION OF SOUND 243 
 
 greuttT. The problem had many interesting aspects, but will best 
 serve the present purpose if for the sake of simplicity and clearness 
 it be held to but one, — the transmission of sound from the servants' 
 dining room in the basement along the great eighteen-inch partition 
 wall up two stories to the insulated bedroom above and opposite. 
 
 It is a fairly safe hazard that the sound on reaching the bedroom 
 did not ciih r l)y way ol' tlic floor, lor I lie combination of reenforced 
 concrete, three inches of sand, three inches of lignolith block, and 
 the wood flooring and carpet above, presented a combination of 
 massive rigidity in the concrete arch, inertness in the sand and 
 lignolith block, imperviousness in the hardwood floor, and absorp- 
 tion in llic padded carpet which rendered insulation pcrlVct, if ])er- 
 fect insulation be possible. No air ducts or steam or water ])ipes 
 entered the room. The only conceivable conununication, therefore, 
 was through the walls or ceiling. The comnumication to the inner 
 walls and ceiling from the surrounding structural walls was either 
 through the air sjjace or through the iron angle bars, which, set in 
 lignolith blocks in the structural wall, retained erect and at proper 
 ilistancf the inner walls. Of the two nu'ans of comnumication, the 
 air and the angle bars, the latter was probably the more important. 
 It is interesting and pertinent to follow this line of comnumication, 
 the masonrv' wall, the angle bars, and the screen walls, and to en- 
 deavor to discover if possible, or at least to speculate on the reason 
 for its exceptional though unwelcome efficiency. 
 
 From the outset it is necessarj' to distinguish the transverse and 
 the longitudinal transmission of .sound in a building member, that 
 is. to distinguish as somewhat ditt'erent processes the transmission 
 of sound from one room to an adjacent room through a se])arating 
 wall or ceiling, fnnu I lie liaiisTiiissioM of sound along tiie floors from 
 room to room, or along the xcrl ical walls from floor to floor. liroadly, 
 although the two are not entirely separable |)lienomena, t)ne is 
 largel\' concerneil in the transmission of the .sound of the voice, or 
 the violin, or of other .sources free from .solid contact with the floor, 
 anil I lie ot her in I lie t raiismission of t he >ouii<l of a i)iano or cello in- 
 struments in direct comnumication with the JMiilding structure — or 
 of noi.ses involved in the oi)erat ion of the i)uil(ling, dynamos, eleva- 
 tors, or the opening and i-losiiig of doors. In the building under con-
 
 244 thp: insulation of SOUNT) 
 
 siileriition. the disturbing sounds were in everj' case communicated 
 directly to the struclure at a considerable distance and transmitted 
 along the walls until ultimately communicated through the angle 
 bars, if the angle bars were the means of commimication, to the thin 
 plaster walls which constituted the inner room. The special features 
 thus emphasized were the longitudinal transmission of vibration by 
 walls, floors, and structural beams, and the transformation of these 
 longitudinal vibrations into the sound-producing transverse vibra- 
 tions of walls and ceilings boimding the disturbed room. Many 
 questions were raised which at the time could be only tentatively 
 answered. 
 
 What manner of walls conduct the sound with the greater readi- 
 ness ? Is it true, as so often stated, that modern concrete construc- 
 tion has contributed to the recent prevalence of these difficulties .'' 
 If so, is there a difference in this respect between stone, sand, and 
 cinder concrete ? In this particular building, the partition wall was 
 of brick. Is there a difference due to the kind of brick employed, 
 whether hard or soft ? Or does the conduction of sound depend on 
 the kind of mortar with which the masonrj' is set ? If this seems 
 trivial, consider the number of joints in even a moderate distance. 
 Again, is it possible that sound may be transmitted along a wall 
 without producing a transverse vibration, thus not entering the 
 adjacent room ? Is it possible that in the case of this private house 
 had there been no interior screen wall the sound communicated to 
 the room would have been less ? We know that if the string of a 
 string telephone passes through a room without touching, a conver- 
 sation held over the line will be entirely inaudible in the room. Is 
 it possible that something like this, but on a grand scale, may happen 
 in a building .'' Or, again, is it possible that the iron brackets which 
 connected the great partition wall to the screen wall magnified the 
 motion and so the sound, as the lever on a phonograph magnifies its 
 motion ? These are not unworthy questions, even if ultimately the 
 answer be negative. 
 
 The investigation divides itself into two parts, — the one dealing 
 with partition walls especially constructed for the test, the other 
 with existing structures wherever found in interesting form. The 
 experiments of the former type were conducted in a special room.
 
 THE INSULATION OF SOUND 
 
 245 
 
 mentioned in some of tlie earlier papers (The Brickbuilder, January, 
 1914),' and having peculiar merits for the work. For an imder- 
 standing of these experiments and an appreciation of the conditions 
 that make for their accuracy, it is necessan,' that the construction of 
 this room be explained at some length. The west wing of the Jeffer- 
 son Physical Laboratory is in plan a large square in the center of 
 which rises a tower, which, for the sake of steadiness and insulation 
 
 Fig. i. Ti'sting Room anil Aiiparatus 
 
 from all external vil)rati<)n, is not merely of indepentlent walls but 
 has an entirely se])arate foundation, and above is spanned without 
 touching by the roof of the main building. The sub-basement room 
 of this tower is below the basement of the main building, but the 
 walls of the latter are carried down to enclose it. The floor of the 
 room is t)f concrete, the ceiling a masonry arch. There is but one 
 door which leads through a small anteroom to the stairs mounting 
 to the 1<'\-<'1 <if I lie l)asemenl of tiic main building. Through the 
 
 ' See page 1!>U, chapter 8.
 
 24G THE INSULATION OF SOUND 
 
 ceilinjj llu're arc two small openings for which special means of closing 
 are provided. The larger of these openings barely permits the 
 passage of an observer when raised or lowered by a block and tackle. 
 It is necessary that there be some such entrance in order that obser- 
 vations may be taken in the room when the door is closed by the wall 
 construction undergoing test. 
 
 Of i)rime importance, critical to the whole investigation, was the 
 insulation between the rooms, otherwise than through the partition 
 to be tested. The latter closed the doorway. Other than that the 
 two rooms were separated by two eigliteen-inch walls of brick, 
 separated by a one-inch air space, not touching through a five-story 
 height and carried down to separate foimdations. Around the outer 
 wall and around the antechamber was solid ground. It is difficult 
 to conceive of two adjacent rooms better insulated, the one from 
 the other, in all directions, except in that of their immediate con- 
 nection. 
 
 The arrangement of apparatus, changed somewhat in later experi- 
 ments, consisted primarily, as shown in the diagram, of a set of 
 organ pipes, winded from a bellows reservoir in the room above, 
 this in turn being charged from an air pump in a remote part of the 
 building, — remote to avoid the noise of operation. In the center 
 of the room two reflectors revolved slowly and noiselessly on roller 
 bearings, turned continuously by a weight, under governor control, 
 in the room above. The chair of the observer was in a box whose 
 folding lids fitted over his shoulders. In the box was the small organ 
 console and the key of the chronograph. The organ and chrono- 
 graph had also console and key connection with the antechamber. 
 The details of the apparatus are not of moment in a paper written 
 primarily for architects. 
 
 Broadly, the method of measuring the transmission of sound 
 through the partitions consisted in producing in the larger room a 
 sound whose intensity in terms of threshold audibility was known, 
 and reducing this intensity at a determinable rate until the soimd 
 ceased to be audible on the other side of the partition. The intensity 
 of the sound at this instant was nimierically equal to the reciprocal 
 of the coefiicient of transmission. This process involved several 
 considerations which should at least be mentioned.
 
 THE INSULATIOX OF SOl^'D 247 
 
 The souiul of known inlt-nsity was producctl l)y organ pipes of 
 know-n powers of emission, allowance being made for the vohnne of 
 the room, and tlie absorbing ])OW('r of the walls. 'I'lic inclliod was 
 fully explained in earlier papers.' It is to be borne in mind that 
 there was thus determined merely the average of intensity. The 
 intensity varied greatly in diil'ercnt ])arts of tlie room because of 
 interference. In order that the average intensity of sound against 
 the partition in a series of observations should e((vial the average 
 intensity in the room, it was necessary to continuously shift the in- 
 terference system. This was accomplished by means of revolving 
 reflectors. This also rendered it possible to obtain a measure of 
 average conditions in the room from observations taken in one 
 position. Finally the observations in the room were always made 
 by the observer seated in the box. as this rendered his clothing a 
 negligil)le factor, and the condition of the room the same wuth or 
 without his presence. Consideration was also given to the acoustical 
 condition of llic anlcchaiiibtT. 
 
 Two methods of reducing the sound have l)een employed. In 
 the one the sound was allowed to die away naturally, the source 
 being stopped suddenly, and the rate at which it decreased deter- 
 mined from the constants of tlic room. In another type of experi- 
 ment the source, electrically maintained, was reduced by the addition 
 of electrical resistance to the circuit. One method was sviitable 
 to one set of contlitions, the other to another. The first was em- 
 ployed in the experiments whose residts are given in tliis jjajxr. 
 
 The first measurements were on felt, partly suggested by the ex- 
 periments of Dr. Damrosch with felt on the walls of the Institute of 
 Musical Art, partly ijecause it offered the tlynanucally simplest jjrob- 
 lem on which to test the accuracy of the method by the concurrence 
 of its results. The felt u.sed was that so thoroughly studied in other 
 acoustical asjjecls in the i)aper i)ublished in the Proceedings of the 
 American Academy of Arts and Scii-nces in liXMi. The tloor separat- 
 ing the two rooms was covered with a one-half inch thickness of this 
 fell, i'lic inlinsity of sounil in I lie main room just audible through 
 the fell was .'{.7 times threshold audibility. Aiitither layer of felt 
 of equal thickness was added to the fii>t, and the reduction in the 
 
 'See liiviTKcriition. pap' 1.
 
 "248 
 
 THE INSULATION OF SOUND 
 
 intensity of sound in i)iissing throngli tlie two was 7.8 fold. Tlirough 
 three-thickness, each one-half, the reduction was 15.4 fold, through 
 four 30.4, five 47.5, and six 88.0. This test was for sounds having the 
 pitch of violin C, first C above middle C, 512 vibrations per second. 
 There is another way of stating the above results which is perhaps 
 of more service to architects. The ordinary speaking intensity of 
 
 10 
 
 .8 
 
 .6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \l 
 
 
 
 
 
 
 \ 
 
 k 
 
 
 
 
 3 
 
 ,2^ 
 
 "-^ 
 
 ^~ 
 
 
 1 
 
 12 3 4 6 6 
 
 Fig. 3 
 
 the voice is — not exactly, of course, for it varies greatly — but 
 of the order of magnitude of 1,000,000 times minimum audible in- 
 tensity. Assimie that there is a sound of that intensity, and of the 
 pitch investigated, in a room in one side of a partition of half-inch 
 felt. Its intensity on the other side of the partition would be 
 270,000 times minimum audible intensity. Through an inch of felt
 
 THE INSl LATIOX OF SOUND ^240 
 
 ils intensity would be 128,000. Through six hiyers of sucli fVlt, that 
 is, through three inches, its intensity would be 11,400 times mini- 
 mum audible intensity, — very audible, indeed. The diminishing 
 intensity of the sound as it proceeds through layer after layer of 
 felt is plotted in the diagram (Curve 1, Fig. 3), in which all the 
 points recorded are the direct results of observations. The intensity 
 inside the room is the full ordinate of the diagram. The curve drawn 
 is the nearest rectangular hyperbola fitting the observed and calcu- 
 lated points. The significance of this will be discus.sed later. It is 
 sufficient for the present i)uri)ose to say that it is the theoretical 
 curve for these conditions, and the close agreement between it and 
 the observed points is a matter for considerable satisfaction. 
 
 The next partition tested was of sheet iron. This, of course, is 
 not a normal building nuiti'rial and it may therefore seem disap- 
 ])ointing and without interest to architects. But it is necessar}' to 
 remember that these were preliminarj' investigations establishing 
 methods and principles rather than practical data. Moreover, the 
 material is not wholly impractical. The writer has used it in recom- 
 mendations to an architect in one of tlK> most interesting and suc- 
 cessful cases of sound insidation .so far underlaktii tliat in an 
 after-theatre restaurant extending imderneal li t lie sidewalk of Broad- 
 way and 42d Street in New York. 
 
 The successive layers of sheet iron were held at a distance, each 
 from the preceding, of one inch, spaced at the edges by a narrow 
 strip of wood and felt, and pressed home by washers of felt. After 
 the practical cases cited at the beginning of the paper, it requires 
 courage and some hardihood to say that any insulation is good. It 
 can only be said thai every care was taken to this end. The results 
 of the experiments can alone measure Hie <fliciency of the inetlK.ii 
 employed, and later they will be discussed with this in view. 
 
 The third series of exi)eriments were with layers of slun-t iron 
 with one-half inch felt occu])yiug part of the air space U-tweeii theni. 
 The iron was that used in the second series, the fell that u.s«'d in the 
 first. The air space was unfortunately slightly greater tliau in the 
 second series, being an inch and a (|uarler instead of an incli. The 
 magnitude of the effect of this ditVerence in distance was not 
 realized at the time, but it was sufhcienl to prevent a direct com-
 
 >.-,0 THE INSULATION OF SOUND 
 
 parisou of the second and tliirtl scries, and an attempt to deduce 
 the latter from the former witli the aid of the first. When this was 
 realized, other conditions were so different as to make a repetition 
 of the series difficuU. 
 
 In the foUowinff tahle is given the results of these three series of 
 experiments in such form as to admit of easy comparison. To tliis 
 end they are all reduced to the values which they would have had 
 with an intensity of sound in the inner room of 1,000,000. In the 
 first column each succeeding figure is the intensity outside an addi- 
 tional half inch of felt. In the second column, similarly, each suc- 
 ceeding figure is the intensity outside an additional sheet of iron. 
 In the third column, the second figure is the intensity outside a 
 single sheet of iron, and after that each succeeding figure is the 
 intensity outside of an additional felt and iron doublet with air space. 
 
 1,000.000 
 
 1,000,000 
 
 1.000,000 
 
 '270,000 
 
 22,700 
 
 23,000 
 
 1'28,000 
 
 8,700 
 
 3,300 
 
 65,000 
 
 4,880 
 
 700 
 
 33,000 
 
 3,150 
 
 220 
 
 21,500 
 
 2,000 
 
 150 
 
 11,400 
 
 1,520 
 
 88 
 
 The sound transmitted in the second and third series is so much 
 less than in the first that when an attempt is made to plot it on the 
 same diagram (Curves 2 and 3, Fig. 3) it results in lines so low as to 
 be scarcely distinguishable from the base line. ^Magnifying the scale 
 tenfold (Fig. 4) throws the first series off the diagram for the earlier 
 values, but renders visible the second and third. 
 
 The method of representing the results of an investigation 
 graphically has several ends in view : it gives a visual impression of 
 the phenomenon; it shows by the nearness with which the plotted 
 values^ lie to a smooth curve the accuracy of the method and of the 
 work; it serves to interpolate for intermediate values and to ex- 
 trapolate for points which lie beyond the observed region, forward 
 or backward; finally, it reveals significant relations and leads to a 
 
 ' In reproducing from the plotted diagrams for Figs. 3, 4, and 5, the dots, in some cases, 
 wliich indicated the plotted values of the observed points, do not clearly appear in distinction 
 on the lines. The greatest divergence, in any case, from the line drawn was not more than 
 twice the breadth of the lire itself.
 
 THE IXST'LATIOX OF SOI XD 
 
 251 
 
 more effective discussion. It is worth wliile thus examining the 
 three curves. 
 
 Attention has already been called to the curve for felt, to its ex- 
 trapolation, and to the close approximation of the observed points 
 to an hyperbola. The latter fact indicates the sinii)lest possible law 
 
 10 
 
 .09 
 .08 
 .07 
 .06 
 .06 
 .04 
 .03 
 .02 
 .01 
 
 12 3 4 6 6 
 
 Fiii. I 
 
 of aliMirplioii. Il |)ro\(s llml :ill l:iyci> aliM)il> III.' -niiir |>n>pt>rt ion 
 (iT llic .soiuid; llial cacli succeeding layer al).sorl)s le.s.s actual .»(>un<l 
 liian tile prcccdiug. l)ut less merely because Ic.vs .souiiil reaches it to 
 be absorbed. In the ca.se in hand the .souiul in pa.vMug through the 
 felt was reduced in the ratio 1.S8 in each layer. :t.."):{ in .ach ukIi. 
 It is customary to tot >U(li curvo by plotting them on a .siH-«ial 
 kiiiii of coordinate i)aper. <>iw «>n whirh, while horizontal <li>- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 1 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 w 
 
 
 
 \ 
 
 
 l~ — — t-.. 
 
 1
 
 <2.n THE INSULATION OF SOUND 
 
 tancc's are iinifonnly scaled as before, vertical distances are scaled 
 with jjreater and greater reduction, tenfold for each unit rise. On 
 such coordinate paper the vertical distances are the power to which 
 10 must be raised to equal the number plotted — in other words, it 
 is the logarithm of the number. Plotted on such paper the curve for 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10 
 
 10' 
 
 10 
 
 10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 '"---. 
 
 ^^ 
 
 ^ 
 
 
 
 
 
 v^ 
 
 
 "^ 
 
 
 .^ 
 
 
 
 \^ 
 
 2 
 
 
 , 
 
 
 
 > 
 
 "^^3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2 3 
 
 Fig. 5 
 
 felt will result in a straight line, if the curve in the other diagram 
 was an hyperbola, and if the law of absorption was as inferred. How 
 accurately it does so is shown in Curve 1, Fig. 5. 
 
 ^^ hen the ob.servations for iron, and for felt and iron, are similarly 
 plotted (Curves 2 and 3, Fig. 5), the lines are not straight, but 
 strongly curved upward, indicating that the corresponding curves 
 in the preceding diagram were not hyperbolas, and that the law of
 
 THE INSULATION OF SOLTND 253 
 
 constant coefficient did not hold. This must be explained in one or 
 the other of two ways. Either there was some by-pass for the sound, 
 or the efficiency of each succeeding unit of construction was less. 
 
 The by-pass as a possible explanation can be c|uickly disposed of. 
 Take, for example, the extreme case, that for fell luid iron, and make 
 the extreme assumption that with the completed series of six screens 
 all the sound has come by some by-pass, the surrounding walls, the 
 foundations, the ceiling, or by some solid connection from the inner- 
 most to the outermost sheet. A calculation based on these assmnp- 
 tions gives a plot whose curvature is entirely at the lower end and 
 bears no relationship to the observed values. In t hr ot lier case, that 
 of the iron only, a similar calcidation gives a similar result; more- 
 over, the much lower limit to which the felt and iron screens reduci>d 
 the sound wholly eliminates any by-pa.ss action as a vital factor in 
 the iron-only experiment. 
 
 The other explanation is not merely necessary bj' elimination, 
 but is dynamically rational. 'J'iie screen walls such as here tested, 
 as well as the screen walls in the actual construction described by 
 way of introduction, do not act by absorption, as in the ca.se of the 
 felt; <lo not act by a process which is complete al the jxiiiil. but 
 rather by a process which in the first screen may be likened to re- 
 flection, and in the second and subsequent screens by a jirocess which 
 nuiy be more or le.ss likened to reflection, but which being in a con- 
 fined space reacts on the screen or screens wliich lia\c i)r(((<l<il it. 
 In fact, the process nuist be regarded not as a sequence of inde- 
 pendent steps or a j)rogre.ss of an independent action, but as that of 
 a structure wliicli must be considered dynamieally as a whole. 
 
 When I lie phenomenon is one of i)ure ab.sorplion. as in felt, it is 
 possible to express by a sim])le fornuiia the intensity of tin- ><>iin<l 1, 
 at any distance x, in terms of the inilial inleiisily 1„, 
 
 I = I„Rk% 
 
 where 11 represents I lie factor of surface discoiil iiiuil\-. and k the 
 ratio in which the intensity is reduced in a unit distance. In the ea.se 
 of the felt tested, R is AHr> and k is :5.j:?, the distance into tlie 
 felt being measiin'd in inches. .\s an ai)|)lication of tiiis f..rnuda. 
 one nuiy compute tlie tliiekne.ss of fell wliieh wouM entirely ex-
 
 '2.54 THE INSULATION OF SOUND 
 
 tin^iiisli ii .soiincl of llic iiilcnsiU- of oriliiiiiry speech, — 10. 4 inches. 
 It is not possible to express by sucli a forniiihi the transmission of 
 sound through either of tlie more complex structures. However, it 
 is possible to e.xtrapolate empirically and show that 10.4 inches of 
 neither would accomplish this ideal residt. although they are both 
 far superior to felt lor thicknesses up to three inches in one case and 
 five and one-half inches in the other. 
 
 A number of other experiments were tried during this preliminary 
 stage of the investigation, such, for example, as increasing the 
 distance between the screen walls, but it is not necessary to recount 
 them here. Enough has already been given to show that a method 
 had been developed for accurately measuring the insulating value of 
 structures; more would but confuse the purpose. At this point the 
 apparatus was improved, the method recast, and the investigation 
 begun anew, thenceforward to deal only with standard forms of 
 construction, and for sounds, not of one pitch only, but for the 
 whole range of the musical scale.
 
 11 
 
 WHISPERING GALLERIES 
 
 It is probable that all existing whispering galleries, it is certain that 
 the six more famous ones, are accidents; it is equally certain that all 
 could have been predetermined without difficulty, and like most 
 accidents could have been improved upon. That these six, the 
 Dome of St. Paul's Cathedral in London, Statuary Hall in the Capi- 
 tol at Washington, the vases in the Salle des Cariatides in the Lou\Te 
 in Paris, St. John Lateran in Rome, The Ear of Dionysius at Syra- 
 cuse, and the Catliedral of Ciirgenfi, are famous al)ove others is in a 
 measure due to some incident of place or association. Four are fa- 
 mous because on the great routes of tourist travel, one because of 
 classical traditions, and one, in an exceedingly inaccessible city and 
 itself still more inaccessible, tlu-oufjh a curious story perjietuated by 
 Sir Jolin W. Herschel in the Encyclopedia Melropolikuui. However, 
 all show the phenomenon in a striking numner and merit the interest 
 wliicli they excite, an interest probably enhanced by the mysterj' 
 attaching to an unpremeditated event in the five more modern cases, 
 and none the less enhanced in the other l)y the tradition of its inten- 
 tional design and as evidence of a "lost art." 
 
 The whispering gallery in the Capitol at Washington is of the 
 simplest possible type. 
 
 The Cajjitol as first built was but the central i)(>rti()n of the i)resent 
 building, the Senate Chamber and the Hail of the IIou.se of Repre- 
 sentatives being at that time innnediately ailjacent to the rotunda. 
 With the admission of new states, and witli tlic general increase in 
 l)opuIation, the Senate and the House outgrew their (piarters. and in 
 ISjI the great wings which now oomiilcte the building were con- 
 structed for their acconmiodalion. Tlir oM Hall of llic House, which 
 in its day must have been acoustically an exceedingly p(H)r assembly 
 room, was transformed into the jjre.sent Hall of Statues and became, 
 or rather remaiiu-d, one of the most perfeet of whis])ering galleries. 
 
 The ceiling of the Ilall of Statues, with the exception of a small 
 circular skylight, is a j)ortion of an exact sphere with its center very 
 
 us
 
 o 
 
 Q 
 
 d 
 
 ^ 
 
 a. 
 a 
 
 5 
 
 en 

 
 WHISPERING GALLERIES 257 
 
 nearly at head level. As shown in the illustrations the ceiling is cof- 
 fered. As originally constructed, and as it remained until 1901, the 
 ceiling was perfectly smooth, being of wood, papered and painted in 
 a manner to n>pre.sent coffering. In lf)01, a fire in the C'lianiher of 
 the Supreme Court, also in the Capitol, led to a general overhauling 
 of the building, and among other dangerous constructions the ceiling 
 of wood in the Hall of Statues was replaced by a fireproof construc- 
 tion of steel and ])laster. Instead of being merely painted, the new 
 ceiling had recessed panels with mouldings and ribs in relief 
 (Fig. 1). In consequence of this construction, the whispering 
 gallery lost a large part of its unique quality. 
 
 During the years preceding the remodeling of the ceiling, the 
 whispering gallery had l)een of great interest to toiu-ists and deep 
 hollows were worn in the marble tile where the observers stood. The 
 experiment was usually tried in either one of two ways. The visitor 
 to the gallery was placed at the center of curvature of the ceiling and 
 told to whisi)er, when the slightest sounds were returned to him 
 from the ceiling. The effect was nnich more striking than one would 
 suppose from this simi)le description. The slight lapse of time re- 
 quired for the sound to travel to tlie ceiling and back, together with 
 one's keen sense of direction, gave the effect of an invisible and mock- 
 ing presence. Or the guide would ])lace the tourists at symmetrical 
 points on either side of the center, when they could with the lu'l[) of 
 the ceiling whisper to each other across distances over which they 
 could not be heard directly, 'i'lie explanation ol' this particular 
 whi.sj)ering gallery is exceedingly simjile. 
 
 Speech, whether whispered or full toned, consists of waves or 
 trains of waves of greatly \ariecl character. The study, to its la>t 
 refinement, of whispering gallery phenomena iii\(>l\(s a coiisitlera- 
 ti(»ii ('f this complicated character ol' .-.pcccli. luil a rough study, and 
 one which serves most ])urp()ses, can be made l)y following the path 
 and the transformation of a single wave. This can be illustrated l)y 
 two series of i)h()fograi)hs. In the one (Fig. 2), the wave is .shown in 
 tiie (litfennt stages of il> advaiKc oulwanl. - si)lierieal, exeej)! 
 where it strikes the floor, the wall, or the repressed transverse arch 
 of the ceiling. In the second series of pholograpiis (Fig. .T). the 
 wave has struck the si.-hericai ceiling everywhere at the same instant.
 
 □□
 
 WIIISPERIXG GALLERIES 259 
 
 and, reversed in direction, gains in intensity as it gathers together 
 toward tlie point from which it issued. The sound reflected from 
 the otlier surfaces may be seen dividing and subdividing in multiple 
 reflection and losing in intensity, while the sound reflected from the 
 spherical ceiling gains througli its rapid convergence. 
 
 These and other similar photographs used in this investigation 
 were taken in a small sectional model, one-sixteenth of an inch to 
 the foot in scale, made of ))laster of Paris or of other convenient ma- 
 terial, and the impulsive report or wave was produced either by the 
 explosion of fulminate of mercury or directly l)y an electric spark. 
 The flash bj* which the exposure was taken had a duratioM of less 
 than a millionth of a second. It is wholly unnecessary for the pur- 
 poses of this present discussion to go into the details of this process. 
 It is sufficient to state that the illustrations are actual jihotographs 
 of real souiid-wa\('s in I lie air and reproduce not iiu rely (he main 
 but the subordinate phenomena. 
 
 Inciting this gallery in an article on Whis])enng (Jalleries in Stur- 
 gis' Dictionarij of Architecture, the writer made the statement that 
 "The ceiling, painted so that it appears deejily panelled, is smooth. 
 Had the ceiling been panelled the reflection would have been irregu- 
 lar and the effect very much reduced." A year or so after this was 
 written the fire in the Capitol occurred, and in order to ])reserve the 
 whispering gallery, whicii jiad l)ecome an object of unfailing interest 
 to visitors to the Capitol, the new ceiling was made "to conform 
 within a fraction of an inch " to the dimensions of the ceiling which 
 it replaced. Notwithstanding this care, the (piality of lh«> room 
 which liad long made it the best and the best known of whispering 
 galleries was in large measure lost. Since then this occurrence has 
 been frequently cited as another of the mysteries of architectural 
 acoustics and a disproof of the ])ossii»ilities of predicting such jjlie- 
 nomena. As a matter of fact, it was exactly the reverse. Only the part 
 betwei-n the panels was reproduced jn the original dimensions of tlie 
 dome. The ceiling was no longer sukioIIi, Die slalT was j)aiiell«-d in 
 real recess and nliif, and the result but confirmed tiie statement 
 recorded nearly two years before ii\ the Dirlionuri/ of Arcliileriiire. 
 
 The loss of this fine whispering gallery has at least some compen- 
 sation in giving a convincing illustration, not merely of the condi-
 
 260 WHISPERING GALLERIES 
 
 tions which make towards excellence in the phenomenon, but also of 
 the conditions which destroy it. The effect of the paneling is obvi- 
 ous. Each facet on the complex ceiling is the source of a wavelet and 
 as these facets are of different depths the resulting wavelets do not 
 conspire to form the single focusing wave that results from a per- 
 fectly smooth dome. In a measure of course in this particular case 
 the wavelets do conspire, for the reflecting surfaces are systeinati- 
 cally placed and at one or the other of two or three depths. The dis- 
 l)ersion of the sound, and the destruction of the whispering gallery is, 
 therefore, not complete. 
 
 An instructive parallel may be drawn between acoustical and 
 optical mirrors : 
 
 Almost any wall-surface is a much more perfect reflector of 
 sound than the most perfect silver mirror is to light. In the former 
 case, the reflection is over 96 per cent, in the latter case rarely 
 over 90. 
 
 On the surfaces of the two mirrors scratches to produce equally 
 injurious effects must be comparable in their dimensions to the 
 lengths of the weaves reflected. Audible sounds have wave lengths 
 of from half an inch to sixty feet; visible light of from one forty- 
 thousandth to one eighty-thousandth of an inch. Therefore while 
 an optical mirror can be scratched to the complete diffusion of the 
 reflected light by irregularities of microscopical dimensions, an 
 acoustical mirror to be correspondingly scratched must be broken 
 by irregularities of the dimensions of deep coffers, of panels, of 
 engaged columns or of pilasters. 
 
 Moreover, just as remarkable optical phenomena are produced 
 when the scratches on a mirror are parallel, equal, equal spaced, or of 
 equal depth, as in mother of pearl, certain bird feathers, and in the 
 optical grating, so also are remarkable acoustical phenomena pro- 
 duced when, as is usually the case in architectural construction, the 
 relief and recess are equal, equally spaced, or of equal depth. The 
 panels in the dome of the Hall of Statues of course diminish to- 
 ward the apex of the dome and are thus neither equal nor equally 
 spaced, but horizontally they are and produce corresponding phe- 
 nomena. The full details of these efiFects are a matter of common 
 knowledge in Physics but are not within the scope of the present
 
 WHISPERING GALLERIES 261 
 
 discussion. It is sufficient to say that the general result is a disper- 
 sion or a distortion in the form of the focus and that the general 
 eflFect is to greatly reduce the efficiency of the whispering gallery, 
 but to by no means wholly destroy it, as would be the case with 
 complete irregularity. 
 
 By the term whispering gallery is usually understood a room, 
 either artificial or natural, so shaped that taint sounds can be heard 
 across extraordinary distances. For this the Hall of Statues was ill- 
 adapted, partly because of a number of minor circumstances, but 
 primarily because a spherical surface is accurately adapted only to 
 return the sound directly upon itself. When the two points between 
 which the whisper is to be conveyed are separated, the correct form 
 of reflecting surface is an ellipsoid having tlie two points as foci. 
 When the two points are near together, the ellijisoid resembles more 
 and more a sphere, and the latter may be regarded as the limiting 
 case when the two points coincide. On the otlicr liaiid. wluii tlie 
 two foci are very far apart the available part of the ellipsoid near one 
 of the foci resembles more and more a paraboloid, and this nuiy be 
 regarded as the otlier extreme limiting case when one of llie foci is at 
 an infinite or very great distance. I know of no building a consider- 
 able portion of whose wall or ceiling surface is part of an exact ellip- 
 soid of revolution, but the great IMorniou Tabernacle in Salt Lake 
 City is a near approximation. Plans of this remarkable building do 
 not exist, for it was laid out on the ground without the aid of fonnal 
 drawings soon after the settlers had completed lluir weary pilgrim- 
 age across the Utah desert and settled in their isolated valley. It was 
 built without nails, which were not to be had, and held together 
 merely by wooden pins and tied with strips of buffalo hide. Not- 
 withstanding this construction, and notwithstanding the fact Uiat it 
 spans 250 feet in length, and 150 feet in breadth, and is without any 
 interior columns of any .sort, it has been free irom the necessity of 
 es.sential rejjair for over fifty years. As the photograph (.Fig. 5) 
 shows, taken at the time of building, the space between the ceiling 
 and the roof is a wooden bridge truss construction. Tlioe photo- 
 graphs, given by the elders of the church, are themselves inter- 
 esting considering the circumsfances uiuler which they were taken, 
 the early dale and the remote location.
 
 1^^ 
 
 l^l^'ni^T 
 
 Fig. i. Exterior. Mormon Tabernacle, Salt Lake City, Utah. 
 
 pK^^rrrrrg 
 
 ^-#^:^.:-^' 
 
 Fig. 5. Photograph showing CoustriKlinii. Muriuoii Tabernacle, Salt Lake City, Utah.
 
 □□ 
 
 Fig. 6
 
 264 WHISPKHIXG GALLERIES 
 
 It is difficult for an interior photograph of a smooth ceiHng to give 
 an impression of its shape. An idea of the shape of the interior of the 
 Tabernacle may be obtained, liowever, from a photograph of its ex- 
 terior. It obviously somewhat resembles an ellipsoid of revolution. 
 It is equally obvious that it is not exactly that. Nevertheless there 
 are two points between which faint soimds are carried with remark- 
 able distinctness, — the reader's desk and the front of the balcony in 
 the rear. 
 
 The essential geometrical property of an ellipsoid of revolution is 
 that lines drawn to any point of the surface from the two foci make 
 equal angles with the surface. It follows that sound diverging 
 from one focus will be reflected toward the other. The preceding 
 photographs (Fig. 6) show the progress of a sound-wave in the 
 model of an idealized whispering gallery of this type in which the 
 reflecting surface is a portion of a true ellipsoid of revolution. 
 
 The most notable whispering gallery of this type is that described 
 by Sir John Herschel in one of the early scientific encyclopedias, the 
 Encydo-pedia Metropolitana as follows: 
 
 In the Cathedral of Girgenti in Sicily, the slightest whisper is borne with 
 perfect distinctness from tlie great western floor to tlie cornice behind the 
 higli altar, a distance of 250 feet. By a most unluckj' coincidence the pre- 
 cise focus of divergence at the former station was chosen for the place of the 
 confessional. Secrets never intended for the public ear thus became known, 
 to the dismay of the confessor and the scandal of the people, by the resort 
 of the curious to the opposite point, which seems to have been discovered 
 by accident 
 
 Aside from the great distance between the foci, the circumstances 
 related had many elements of improbability and the final discussion 
 of this subject was postponed from year to year in the hope that the 
 summer's work, which has usually been devoted to the study of Eu- 
 ropean auditoriums, would carry the writer near Girgenti, an inter- 
 esting but rather inaccessible city on the southwestern coast of 
 Sicily. Finally, failing any especially favorable opportunity, a flying 
 trip was made from the north of Europe with the study of this gallery 
 and of the Ear of Dionysius at Syracuse as the sole objective. On 
 the way down the perplexity of the case was increased by finding in 
 Baedeker the statement that there is a noteworthy whispering gal-
 
 M 
 
 Klii. ;. lilliTl'T. ( allinlricl •'( (iiri^'liU. >li lis
 
 200 WinSPERIXG GALLERIES 
 
 lery between the west entrance of the Cathedral and "the steps of 
 tlie liigh altar." Such a whisppnnf:r fjallery is wholly inconceivable. 
 The facts showed a whispering gallery between the foci as described 
 by Herschel, altliongh the accompanying story is rendered improb- 
 able by the extreme inaccessibility of the more remote focus, and its 
 very conspicuous jiosition. Nor is the distance so great as stated l)y 
 Herschel, being a little over 100 feet instead of 250 feet. However, 
 the interest in this whispering gallery arises not because of any inci- 
 dent attending its discovery, but because it illustrates, albeit rather 
 crudely, the fonn of surface giving the best results for whispering 
 between two very widely separated points. 
 
 As already stated the strictly correct form of surface for a whisper- 
 ing gallery is an ellipsoid of revolution whose foci coincide with the 
 two points between which there is to be communication. In the 
 whispering gallery in the Cathedral of Girgenti (Fig. 7), the focusing 
 surface consists of a quarter of a sphere prolonged in the shape of a 
 half cylinder fonning the ceiling over the chancel. This is obviously 
 not a true paraboloid, and, such as it is, it is interrupted by an arch 
 of slight reveal where the cylinder joins the sphere; moreover, the 
 two points of observation do not lie on the axis of revolution as they 
 shovdd for the best result. But a hemisphere and a continuing cylin- 
 der make a fair approach to a portion of a paraboloid; and while the 
 two points of observation are not on the axis of revolution, they are 
 on a secondary axis, the station by the door being below, and the 
 focus in the chancel being at a corresponding distance above the 
 principal axis. 
 
 In all the preceding galleries, there is but a single reflection be- 
 tween the radiant and the receiving foci. There are others in which 
 there are several such reflections. \Yell-known examples are the 
 church of St. John Lateran in Rome and in the Salle des Cariatides 
 in the Louvre. 
 
 In the Church of St. John Lateran (Fig. 8), each bay in the great 
 side aisles is a square having a ceiling which is approximately a por- 
 tion of a sphere. At best, the approximation of the ceiling to a sphere 
 is not close and the ceiling varies from bay to bay, not intentionally 
 but merely as a matter of variation in construction. In one bay more 
 closely than in the others the ceiling, regarded as an acoustical
 
 c 
 
 5 
 
 K 
 3
 
 2(iS AVHISPERIXG GALLERIES 
 
 mirror, has its i'uci Hourly at lioad level. In consequence of this, two 
 obser^•ers standing at opposite corners can whisper to each other 
 with liic ceiling as a reflecting surface. The curvature even in this 
 bay is not ideal for the production of a whisj)ering gallery, so that 
 thus used the gallery is far from notable. It so hai)pens, however, 
 that the great square columns which form the corners of each bay 
 have, instead of sharp corners, a reentering cove or fluting in the arc 
 of a circle and over twelve inches across in opening. If the observers, 
 instead of attempting to speak directly to the ceiling, turn back to 
 back and face the columns standing close to them, this great fluting 
 gathers the sound from the speaker and directs it in a concentrated 
 cone to the ceiling; this returning from the ceiling to the opposite 
 angle of the bay is concentrated by the opposite fluting on the other 
 obser^'er. In more scientific language, borrowed from the nomencla- 
 ture of the makers of optical instruments, the flutings increase the 
 angular aperture of the system. 
 
 An almost exact duplicate of this whispering gallery is to be found 
 in the vestibule of the Conservatoire des Arts et INIetiers in Paris. 
 This vestibule, itself also an exhibition room but called since the dis- 
 covery of its peculiar property La Salle-Echo, is square with rounded 
 corners and a low domical ceiling. Here, as in St. John Lateran, the 
 observers face the corners and the whisper undergoes three reflec- 
 tions between the foci. The fact that the two observers are back to 
 back diminishes the sound which would otherwise pass directly be- 
 tween them and makes the whispering gallery more pronounced and 
 the phenomenon much more striking. In both galleries it is the cus- 
 tom for the observers to take their positions in a somewhat random 
 numner. The correct position is at a distance from the concave 
 cj'lindrical surface a little less than half the radius of curvature. 
 
 In these whispering galleries the surfaces are not theoretically cor- 
 rect and the phenomenon is far from perfect. This failure of loud- 
 ness and distinctness in most of the multiple reflection galleries arises 
 not from any progressive loss in the many reflections, for the loss of 
 energy in reflection is practically negligible. Indeed, given ideally 
 shaped surfaces, multiple reflection whispering galleries are capable 
 of producing exceptional effect; for if two of the surfaces be very 
 near the observers they may, even though they themselves be of
 
 Fio. II, Salic <lc8 Curiatiilc*. llic I»uvrr, I'arii.
 
 070 WHISPERING GALLERIES 
 
 small clinu-nsions. gather into the phenomenon very large portions of 
 the emergent and of the fociLsed whisper. In both St. John Lateran 
 and La Salle-Echo, the condensing mirrors are cylindrical and gather 
 the sound horizontally only. In the vertical plane, they are wholly 
 without effect. 
 
 It is not difficult to determine the correct forms for the extreme 
 mirrors. If the ceiling be flat, the reflecting svu'faces near the two 
 observers should be parabolic with the axis of the ]}araboloid di- 
 rected toward the center of the ceiling, the correct position for the 
 mouth of the s])eaker and the ear of the auditor being at the foci of 
 the two paraboloids. If the ceiling be curved, the simplest design is 
 when the first and last reflector.s are portions of an ellipsoid, each 
 with one focus at the center of the ceiling and the other at one of the 
 foci of the system as a whole. Einally, if the ceiling be curved, there 
 is still another theoretical shape for the end reflectors, determined by 
 the curvature of the ceiling; in this case the ideal surface is not a 
 conic surface, nor otherwise geometrically simple, but is such that the 
 converging power of the end mirror with half the converging power 
 of the middle mirror will give a plane wave. 
 
 It is obvious that the accurate fulfilling of these conditions by acci- 
 dent is improbable, but they are at least api)roached in the whisper- 
 ing gallery in the Salle des Cariatides in the Louvre (Fig. 9). Along 
 the axis of the room, and at no inconsiderable distance apart, are two 
 large shallow antique vases. A whisper uttered a little within the rim 
 of one is partially focused by it, is still further focused by the barrel- 
 shaped ceiling, and is brought to a final focus symmetrically within 
 the rim of the f lu-ther vase. It is evident that the effect is dependent 
 on only a portion of each vase, but this portion satisfies the necessary 
 conditions to a first approximation in both longitudinal and in trans- 
 verse section. When the correct foci are found this whispering gallery 
 is very distinct in its enunciation. It would be even more distinct if 
 the ceiling of the room were slightly lower, or, keeping the height the 
 same, if its radius of curvature were slightly greater. It would be 
 still better if the vases were slightly deeper. 
 
 The whispering gallery which has received the greatest amount of 
 discussion, and a discussion curiously inadequate in view of the emi- 
 nence of the authorities engaged, is the circular gallery at the base of
 
 Via. 10. Section ihrouRli Doim- ..f St. I'lmli. Cntholnil. I^.ml..n
 
 272 WHISPERING GALLERIES 
 
 the dome of St. Paul's Cathedral in London. This gallery was first 
 brought into scientific consideration by Sir John Herschel, who in 
 describing it stated that "tlie faintest sound is faithfully conveyed 
 from one sitle to the other of the dome, but is not heard at any inter- 
 mediate point." According to Lord Rayleigh, whose reference, how- 
 ever, I am unable to verify, and either in page or edition must be in 
 error, an early explanation of this was by Sir George Airy, the Astron- 
 omer Royal, who "ascribed it to the reflection from the surface of the 
 dome overhead." Airy coidd have been led into such error only by 
 the optical illusion whereby a dome seen from within seems lower 
 than it is in reality. A moment's inspection of the preceding 
 illustration (Fig. 10), which the Clerk of the Works kindly had re- 
 produced from an old engraving in the possession of the cathedral, 
 shows that this explanation would be incorrect. The guide who does 
 the whispering usually occupies the position marked "A"; the other 
 focus is in the position marked " B." The focus accounted for by Airy 
 would be high up in the dome. Lord Rayleigh taking exception both 
 to the statement of fact by Herschel and the explanation by Airy 
 wrote " I am disposed to think that the principal phenomenon is to be 
 explained somewhat differently. The abnormal loudness with which 
 a whisper is heard is not confined to the position diametrically oppo- 
 site to that occupied by the whisperer, and therefore, it would appear, 
 does not depend materially upon the symmetry of the dome. The 
 whisper seems to creep around the gallery horizontally, not neces- 
 sarily along the shorter arc, but rather along that arc toward which 
 the whisperer faces. This is in consequence of the very unequal 
 audibility of a whisper in front of and behind the speaker, a phe- 
 nomenon which may easily be observed in the open air." Lord 
 Rayleigh's explanation of the phenomenon in this case as due to the 
 "cree{)ing" of the sound around the circular wall immediately sur- 
 rounding the narrow gallery accessible to visitors is unquestionably 
 correct. It is but another way of phrasing this explanation to say 
 that the intensification of the sound is due to its accumulation when 
 turned on itself by the restraining wall. It is obvious that the main 
 intensification arises from the curved wall returning on itself. Verti- 
 cally, the sound spreads almost as it would were the curved wall 
 developed on a plane. This vertical spreading of the sound is in a
 
 "WIITSPERIXG GALLERIES 273 
 
 measure restricted by the circular floor gallery and by the overhang- 
 ing ledge of the cornice moulding. The cornice can be made to con- 
 tribute most to the effect by nuiking the oirve of its lines below the 
 principal jjrojecting ledge, liiat which corresponds to the drij) mould- 
 ing of an exterior cornice, relatively smooth and sinijjle. 
 
 But even Lord Rayleigh's ex])lanation does not fully account for 
 the truly remarkable (lualities of this whispering gallery, 'llu-re are 
 many circular walls as high, as hard, and as snu)oth as that in St. 
 Paul's (iallery but in which the whispering gallery is not to be com- 
 pared in quality. The rear walls of many semi-circular auditoriiuns 
 satisfy these conditions without jjroducing jiarallel results, for ex- 
 ample in the Fogg lecture-room at Harvard I'niversity l>efore it was 
 altered, and in the auditorium just completed at Cornell I'niversity. 
 A feature of the whispering gallery in St. Paul's, contributing not a 
 little to its efficiency, is the inclination of its wall, less noticeable per- 
 haps in the actual gallery than in the architectural " Section." The 
 result is that all the st)uiul which ])asses the (|uarter point of the 
 gallery, the ])oint half way around Ix-tween the foci, is brought down 
 to tlie le\('l of tlie observer, and, ((iiiilniicd with the reflection from 
 the ledge which constitutes the broad seat running entirely around 
 the gallery, confines and intensifies the sound. This feature is of 
 course of unusual occurrence. 
 
 It may not be out ot iilace to give the dimensions of this gallery. 
 The distance from focus to focus, if indeed in this type of gallery 
 they can be called foci, is 1.50 feel. The wall ha> a height of -2(1 feet, 
 and is not moulded in panels as shown in the engraving, i)ut is smooth 
 except for eight shallow niches. While the inclination of the wall in 
 the gallery of St. Paul's is a contributing factor, an even nu)re etticient 
 wall would have been one very slightly, imleed almost impere«'i)tibly, 
 curved, the section being the arc of a circle struck from the center of 
 the dome on a level with the ob.servers. Such a gallerj' will be in the 
 dome of the Missouri State ("apilol, a gallery uni<|ue in this respect 
 that it will have been planned intentionally by the architects.' 
 
 A discussion of noted whimpering galleries would not l)e nMuph-le 
 
 ' The liiiililiiiK is iii.w (tmipl.l.- t)m- ..f llir anlill.-. In. Mr. F:,1k<t1..ii S««rl»..ul. rriH.rl. 
 that tlie wliisprriiig galkr.v in tin- .Inmr .xiutly fiillilU I'n.f.-vvir Sal.iiir'. pn>lK-ti.>n. ami 
 liB.s been the cause of much curionity nnd n.iloiii.tlimcnt. — hxlitor.
 
 "274 
 
 WIIISPERLXG GALLERIES 
 
 witlunil iiK'iilioii of llio famous Ear of Dionysius at Syracuse. A 
 mile out from the present city of Syracuse, on the slope of the terrace 
 
 occupied by the Neapolis of 
 the ancient city, are the re- 
 mains of a quarry entered 
 on one side on the level but 
 cut ])ack to perpendicular 
 walls from a hundred to a 
 lumdred and thirty feet in 
 lieight. 'J'his old ((uarry. 
 now overgrown by a wild 
 and luxurious vegetation, is 
 known as the Latomia del 
 Paradiso. At its western 
 angle is a great grotto, 
 shaped somewhat like an 
 open letter S, 210 feet in 
 winding length, 74 feet high, 
 35 feet in width at the base 
 and narrowing rapidly to- 
 ward the top. The inner- 
 most end of this grotto is 
 nearly circular, and the 
 rear wall slopes forward as 
 it rises preserving in revolu- 
 tion the same contour that 
 characterizes the two sides 
 throughout their length. 
 The top is a narrow channel 
 of a uniform height and but 
 a few feet in width. At the 
 innermost end of this chan- 
 nel, at the apex of the half 
 cone which forms the inner 
 end of the grotto, is a verti- 
 cal opening four or five feet square, scarcely visible, certainly not 
 noticeable, from below. This opening is into a short passageway 
 
 Fig. 11. Plan and Elevation, with Sectional 
 Indication, of Ear of Dionysius, Syracuse, 
 Sicilv.
 
 Fig. \i. View of Oiitcr 0|icDing, the SoK-allorl Kar ut Uionyiiui, Syr»ru»r. Sirilj .
 
 276 WHISPERIXG GALLERIES 
 
 which k'ads to a fliglit of steps and thence to the ground above (Fig. 
 11). The grotto is noted for two somewhat inconsistent acoustical 
 properties. When being shown tlie grotto from below, one's atten- 
 tion is called to its very remarkable reverberation. When above, 
 one's attention is called to the ability to hear what is said at any 
 point on the floor. 
 
 It is related that Tyrant Dionysius, the great builder of Syracuse, 
 so designed his prisons that at certain concealed points of observation 
 he could not merely see everything that was done, but, through re- 
 markable acoustical design, could hear every word which was spoken, 
 even when whispered only (Fig. 12). There is a tradition, dating 
 back however only to the sixteenth century, that this grotto, since 
 then called the Ear of Dionysius, was such a prison. Quarries were 
 plausible prisons in which captives of war might have been com- 
 pelled to work, and there are, surrounding this quarry, traces of a 
 wall and sentry houses, but there is no direct evidence associating 
 this grotto with Dionysius, unless indeed one regards its interesting 
 acoustical properties taken in connection with classical tradition as 
 such evidence. 
 
 In its acoustical property this grotto resembles more a great ear 
 trumpet than a whispering gallery in the ordinary sense of the word. 
 It is, of course, in no sense a focusing whispering gallery of the type 
 represented by the vases and curved ceiling in the Louvre. It more 
 nearly resembles the gallery in St. Paul's Cathedral, but the sound 
 is not spoken close to the deflecting wall, one of the essentially 
 characteristic conditions of a true whispering gallery of that type, 
 and tlie wall is not continuously concave. In fact, in other ways also 
 its acoustical property is not very notable, for distinctness of enun- 
 ciation is blurred by excessive reverberation. 
 
 It is conceivable that whispering galleries should be of use and 
 purposeful, but it is more probable that they will remain architectural 
 curiosities. When desired, they may be readily woven into the design 
 of many types of monumental buildings.
 
 APPENDIX 
 
 NOTE OX MKASIHKMKNTS Ol' TlIK INTFASITV OF SOIM) WD 
 ON rilK HKACTIO.N OK lliK HOOM ll'ON THK SOIM) 
 
 Uiuixc one of lluM';irlyl<'ctiin's jjivi-n at the Sorhoniu- in llu- spriiif,' 
 of 1917, rrotV.ssor Sal)iiU' n-frnvd to tlu> diiiicullit-.s iiilnTt-nt in t-x- 
 pcriments on sound intensities. The following; is a free translation 
 from I lie Holes, in French, whiili lie iJiipand for tliis lecture: 
 
 In no other donian have physicists disregarded the conditions in- 
 troduced by the surrounding materials, hut in acoustics these do not 
 seem to have received the least attention. If measurements are made 
 in the o])en air, over a lawn, as was done by Lord Rayleigh in Cfrlain 
 experiments, is due consideration given to the fact that the surface 
 has an absorbing power for ^()Ull(l of from 40 to 00 percent? Or, if in- 
 side a building, as in Wieu's similar experiments, is allowance made 
 for the fact that the walls reflect from i):3 to 08 percent of the souud? 
 We need not be surprised if the results of such ex|)eriments ditfer 
 from one aiiollici' l)y ;i fiicloi' of inorc Ihaii :i liuiidred. 
 
 II would i)c no nior<' ali^urd to carrA' out photometric nieasure- 
 meuls ill a room where the wails, ceiling, and even the floor and tables 
 consisted of highly polished mirrors, than to make mea>uremeut> on 
 the intensity, or on the (plant it at ive analysis of .sound, under the con- 
 ditions in wliicli sucli e\|)eiiiiieiits have almost iuvariaidy been exe- 
 cuted. It is not astonishing that we have been discouraged by the 
 results, and that we may have des])aire(l of seeing acoustics iH-cupy 
 the ijositioii to which it rightly belongs among the exact .sciemvs. 
 
 'I'lie leiiglli of I lie Waves of ligiit is so small compared with the 
 dimensions of a photometer I liat we do not need to conn-rn ourselves 
 with the plieiiomeiia of interfercuee while measuring the intensity of 
 light. In the case of sound, however, it mu>t be (juite a dilTer»-nl 
 matter. 
 
 III Older to show lliis ill a definite manner. I have niea.surv«l tlie 
 iuteiisily of the sound in all parts of a certain laboratory nK.m. For 
 simplicity, a .symmetrical room was .selecteil, and the sount-, giving ii 
 very pure tone, was placed in the center. It was fouiul that, near tlu*
 
 '278 APPENDIX 
 
 source, oven at tlio soiinr itself, the intensity was in reality less than 
 at a distance of five feel from the source. And yet, tJie clever experi- 
 menter, Wien, and the no less skillful psychologists Wundt and 
 Miinsterberg have Jissumed under similar conditions the law of varia- 
 tion of intensity with the inverse square of the distance. It makes 
 one wonder how they were able to draw any conclusions from their 
 measurements. 
 
 Not only do the walls reflect sound in such a way that it becomes 
 many times more intense than it otherwise would be; and not only 
 does the interference of soimd exist to such an extent that we find 
 regions of maximum and regions of minimum of sound in a room; but 
 even the total quantity of sound emitted by the source itself may be 
 greatly affected by its position with regard to the intierference system 
 of the room. 
 
 This will be more readily understood if illustrated by an incident 
 drawn from the actual experiments. A special sort of felt, of strong 
 absorbing power, was brought into the room and placed on the floor. 
 The effect was two-fold. First, the introduction of the felt increased 
 the absorption of the sound, and thus tended to diminish the total 
 intensity of sound in the room, theoretically to a third of its previous 
 value. But actually it had the contrary' effect; the sound became 
 much louder than before. The felt was so placed on the floor as to 
 shift the interference system in the room, and thus the reaction of the 
 sound vibrations in the room upon the source itself was modified. 
 The source was a vibrating diaphragm situated at the base of a res- 
 onating chamber. In its first location, the source was at a node of 
 condensation, where the motion of the sound which had accumulated 
 in the room coincided with that of the diaphragm. It was thus diffi- 
 cult for the diaphragm to impart any additional motion to the air. 
 In the second case, however, the vibrations of the two were opposite; 
 the diaphragm was able to push upon the air, and although the am- 
 plitude of its motion was somewhat reduced by the reaction of the air 
 upon it, the emitted sound was louder. When under these conditions 
 the diaphragm was forced to vibrate with the same amplitude as at 
 first, the emitted sound became eight times louder. 
 
 Naturally these two positions in the interference system were de- 
 signedly selected, and they show exceptional reactions on the source.
 
 AITFADIX 279 
 
 However, in tlie case of a very eoin|)lex sound, a eoni]>araljle iliver- 
 gence in the reaction of tlie room on the different conipon<nt.s of tlie 
 sound would be probable. 
 
 It is thus necessary in quantitative research in acoustics to take 
 account of three factors: the effect of reflection by the walls on the 
 increase of the total intensity of sound in the room ; the effect of inter- 
 ference in greatly altering the distribution of this intensity; and the 
 effect of the reaction of the sound vibrations in a room upon the 
 source itself. . . . 
 
 In choosing a source of sound, it has usually been assumed that a 
 source of fixed amplitude was also a source of fixed intensity, e. g., a 
 vibrating diaphragm or a tuning fork electrically maintained. ( )n t In- 
 contrary, this is just the sort of source whose emitting power varies 
 with the ])osition in which it is placed in tlie room. On the other 
 hand, an organ pipe is able within certain limits to adjust itself auto- 
 matically to the reaction due to the interference system. We may 
 say, simj)ly, that the best standard source of sound is one in which the 
 greatest percentage of emitted energy takes the form of sound.
 
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