COLLECTED PAPERS ON ACOUSTICS WALLACE CLEMENT SABINE ¥■' -.*'' "* ■ ' . t.'.. rv n t !'■ I * '9.' ■?■ r^ /P. 2)7 ^ -^i<_-«i<_ ^^e^^c-^ //t 2_ 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. PniXTED AT THE HARVARD UXIVERSITV PRESS CAMBRIDGE, MASS., U. S. A. 'NA2S00S121922 HIIIIIIIIIIJIUIJI L 006 267 198 7 D 000 580 671 6 If i.