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e'

RESEARCH IEP~.RTI:ENT

EXPERUml\fTS ON THE HELAfJ:IVE EF:B'ICIENCY OF CYLnmHICAL AND HECTANGUIJAH Dn'FUSERS

F. L. Ward LE. Hnndall

F.L. Ward

Report No. B.058 Serial No. 1953/29

(w. ~~octor Wi:son)

CONFIDENiCIA1

Research Department October9 1953

1.

EZPERU;Elirrrs ON Q.1HE RELNrIVE KBTF'IC IENCY

Figs. Nos • . B.058.1 to B.058.9

•• ______________ ..... ___ • __ -.... .... __ ."~~_-~~._., ____ "_o~. __ •• ~'_~ ___ .~~"'_

OF CYIJIJIIDRICAI, Al:ifD .l:l.ECTANGUIJAR DIF:FUSER8 ____ .. _ .~ -.-._ •• _ ..... __ .~.-- • __ ~ _._ r _______ • ___ ._. ___ -.~_ ..... ____ ~ ____ . ___

Expe:L'iments on the effects of rectangular and hemicylindrical wall irregt.llarities on the diffusiorc of sound in a talks studi0 and a small reverberation room are described in this report. f1'he results in the studio were inconclusive 9 owing to tho fact that the walls were insuff:1,ciently insulating~ those in the reverberation room confirmed previous findings that rectang·l.llar shapes are more efficient as diffusers than hemicylindrical.

Introduction

In a previous paper(l) are eiven the results of an investig'ation of the relative .efficiencies as sound diffusers of several type.3 of wall irregularity.

A small model was used, the frequency of the sound being incl'eased in inverse proportion to the model scale to maintain a correct ratio of vvavelen(~th to mo,lel dimensions. To simplify the conditions 9 one dimension of the mode 1 was made very mUC;l smaller than the others. The diffusers were made in the for'11· of cylinders or prisms parallel to this dimension, and having semicircular 9 rectangular and triangular sections. Hectangular prismsllvere found to be more effective than other shapes of the same cross .... sectional n.rea. This reSU.L t is In agreeme(~)with,the conc:::"11.sions of a subsequent mathematical treatment by Head • Q.'he :'.nvestieaticn has been extended to three dimensions 9

using reoms of 30 to 5;] m3 volume (900 - 1500 ft 3) and diffusers taking the form of rectangular parallelopipeds and short hemi-cylinders with flat ends.

2. Diffuse and Undiffused Sou:nd· .. Fields ~. ______ ~~~" ___ ".. __ __ <~ ____ .""'---___ ._N ____ M ______ .~._._ ~6 _____ , ___ ~_.~ ___ -.::-

A sound field is denned as beine completely diffuse (3) if it has uniforn1 e:lergy denslty within the region consiclered and if the directions of propagation at allY arbitrarily selecterl points arel,"holly raLdom in distribution. '1'his state 0f complete diffusion was assumed in the deriva.tion of the classical reverberation formulae for the reverberation

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time of a room but it does not occur in practice. The sound pressure at any point in the room is a vector summation of tho pressure of a number of reflected waves, the relative phases of which will vary with t1:1e position in the room as well as with the frequency of the sound.

This may be illustr[ted by r3fernnce to the simple case of a duct or organ pipe in which resonances OCCllr at all ]requencies for which the lenr;th of the duo t is an even number of half-w'1velengths. rrhe pressure at any point will vary with the frequency? and <.it any given resonance ireqw:mcy +he pressure will vary from point to point along the standing wave system, one effect being coro.plementary to the other.

Imperfect diffusion may thArefor8 appear in at least two measurable forms, (1) as a change in pressure with a change of posi tion? the freq'wncy of the sound. remaining constant 9 and (2) as a chanc;e in preS;Jure with change in frequency? the p08i tions of source and receiver remaining unchanged.

In the case of the duct, the resonan(;e frequencies are separated by comparativel;y wide intervals and the sound pressure will vary considerably from point to point in a single standing­"vave system. '1'hero will therefore be large changes of p:.'essure wi th frequency and posi t:LOl~9 indicating very poor diffusion. In a room? however 9 particularly a-0 high frequencies 9 the number of modal frequencies becomes so large that the pressure at any point will represent tile random summation of tho contributions from a large number of standing-wave systems ai1d a more diffused field results.

'1:he response of a room to a short pulse of sound cEtn)be shown to be related directly to the s~eady-stete effects\4 • Imperfect diffusion. indicateC: in the steady-state measurements by variations of pressvre with freq'l:.ency or position, is shown by deviations in the press'..lre/time relation from an exponential decay curve. )';ol'eover, if the sound-field is highly diffuse the energy distribution over the region will be (oL1f::tant not only in the steady state 9 but throughout the period of tl18 sound decay after the source has cea8ed to radiate. The rate of decay will thus be constci,nt throughout the room, and throughout the frequency range ~ provided that there are· no chanGes of abso:L'ptioll with frequency. 'l'he variation of reverberation time with position is therefore a measure of the state of diffusion and has certain practical advantages for this purpose.

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other quantities such as the vari~tion with p0sition in the type of decay of a short pulse may be useful indications of diffusion under certain condl tions. The frequency-·spacing of the modes of osc5.1-lation of a room decreases as frequency or the size of the room increases 9 and results in an increase of diffusion. IJ:1he difrusion depends also on the general shape of the rooffi 9 being :east when the room is a parallelopiped sin/ie the modes are least complex for this figure. Any changes in the sha1)e of the walls 9 such as the addition of pro jections 9 which increase t~le complexity of the modes 9 will reduce the spatial or frequency separation of the pressure caxima and lead tr a higher statistical uniformity. These are the conclltions necessary for a high degree of diffusion.

It vrill be seen U,a t the efficiency of such projections in producing a state of high dif=:J.s~_)n is measured bY9 and can only be considered in relation ii09 the s-~anding-wave field in the room. It follows that u, study of diffusers in free-field conditions is of very little interest unless the effects can be directly interpreted in tEfrJ~1S 0:: thelr ef:"'ect in a reverberant enclosure. l![eyer and Bohn\5) have recer.tly carried out such an investigation v~1ich showed that cylil"clrical diffusers were most effective. However 9 since the necessary theoretical linl:: betvveen free--field and reverberant conditions is abseflt9 the results have no direct bearing on the efficiency of the diffusers as diffusion is here defined.

To summarise 9 ~he effeGt of wall irreb~larities in promoting diffusion can only be measured in relation to the sound-field in a rOOfii. Some of the effects vrhich ma;y be used as me~sures of the departure from truly diffuse conditions are the following;--

(1) (2 ) (3 ) (4 )

(5)

(a)

Variation of sound preSBure with frequency Varia tion of sound pressure with posi tioy. Ve,riation. of reverbelation time with positil,;n rrhe irregular:.ty of th(' envelope of the decay of a shr;rt pulse of sound Variation of short pulse decay irregularity with position.

Nethod

In the previous investigation(l) a quantity called the "line irrec.,~lari ty" ef thA steady state frequency characteristic was used as an index of diffusion. Although a convenient afld useful quantity for that particulc:.r inves-tigation9 it has disadvantages when applied

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to ro~ms in general. In particular tl18 scale vartes Wl"0l1 the frequency range considered and an approxtmate correction only can be made.

I"or these reasons it Nas decided to measure transmisBion trregularity (\f the steaq.t-)stat~ frequency characteristic as denned by Bolt and Roop\ • ThLs quantity is the sum of all the changes in level, irres'pective of sign, which OCC1..<r when an exciting tone is slowly changed in frequency. The disadvantage ef this parameter is the great labour entailed in deriving it frorH a recorded steady-state characteristic. An automatic analyser was therefore built +'0 carry out the summation directly without recourse to recording and f,rraphtcal measurement.

The basis of the inotrument is a hich-speed level recorder of tlce Neumann or Jrtiel and Kjaer type in which a recording stylus marks a waxed pape:r. 'Hle stylus of the recorder ts rpplaced by a lightly sprung phosphoy-bronze contact arm which travels over a contact strip.

The contact strip (shown in F'ig. 1) consists of 100 leaves of copper Sel'larated from each other by mica spacers. T'.le edges of o'lternate copper leave;) form 50 contacts over which the bronze wiper travels~ while the other 50 leaves are connected together to serve as elE;ctrical scrOC3l1s. T}w distance -oetween each two successive contact st:ips corresponds to I db level change in the recorder, and the total change of level, irrespective of sign, may thereforo be. measured ever any given interval of time by counting the number of times the wtpor touches a fresn contact on the strip. The Jesign of the automatic counter is descrlbed in the Appendix.

(c) Pr!'llifl1..i.y!"D£LELx.?~_r_iE13JE.~_~_~ __ ~!..(e_~_"L. o~ __ 'p_~~n.2t_n_Li_n __ th_~ Recorder

The first measurements in an experime~ta: studio (G12 Nightingale SCiuare) were intended as pilot experiments to test the technique. Tone slowly sweeping in frequency from 300 cls to 1500 cls was radiated from a loudspeaker in the Corner of the studio while the output from a SoT. and 0. 402lE omnidirectional microphone was taken to a level.recorder fi tted with tLe analyse:!. A hiCh pass filter was used to reduce low frequency no~se due mainly to vibrcdion in the building.

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A reading of tho counter wns made at interva-Ls of 100 c/s. It was found that the derived value of the irre§,"Ularity was critically dependent on the damping of the level recorders. This type of recorder has a tendency to "overshoot" when a rapid dip in the transmission curve oucurs; high damping ma;,/? on the other hand? reduce the writing speed to too low a value. Experiments were made to find the correc~ adjustr:lents and these were used for later measurements.

To preserve stendy state condi ijiQns the freCluency must not be changed too Cluickly. Bolt and Roop\6} have given a criterion for the maximum rate of freCluency sw~ep;

vvhere R == ra to of svveep kn == damping constant of the nth normal mode.

\!\Then the whole room is being considered? kn may be replaced by the Sabine theory damping constant? k? given by

k (c ol S)/SV (2 ) where S surface area of

10 the walls of

3 log the room e (3) c(== ::=. _ . ....--._ .. _------ mean absorption er coefficient

V volume of room c = velocity of sound er reverberation

By substit.u.tion ill eClllation (1) we have~

2 R ~ 18/T c/s per sec.)

all Cluantitie8 being in cogos. units.

For a reve"'beration time of 0.6 seconds? the maximum value in the studiO) the maximum rate of sweep is thus about 50 c/s per second. In practice the limit was set by the level recorders which vvere incal,able of following the fastest level changos accurately above 1500 c/s.

time

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The irregularity is considerabl;y dependent upon reverberation time. This was estahlished in the model experiments and has also been pointed out by Bolt anu lloop (see Appendix 2)~ whose Correc­tions for the effect9 however? arG not well enough substantiated 'Jy experiment to be reliel upon. An experiment was therefore made in the studio described in Research Report E.047 to determine the effect of changing the reverberation time in a ratio of about 2 1. '1'he r3sults? also given in Appendix 2~ showed that within experimental limits) the irregularity was proportional to the reverbera ti on time) other variable s remB.ining c :::ms tant. In subsequent measurements) the reverberation time was made as nearly as possible the same for all the experimental wall conditions and residual variations were corrected by making use of this proportionality.

(f) .~.l_s_e_ JF.:r::c.~JaF.~~tx- }T~_ap . .lF?!n.ep_t_~.

In the investiga tiOl1 (1) alread~r referred to 9 the resr'onse of a model to short pulses was used as a rueasure of the state of diffusion. In aPJlly~~ng this method in rooms of normal size however? it was not found possible to use pulses short enough to allow the echoes to remnin distinct. Both spark and locdspeaker sources were tried) and tte final arrangement? by which a pulse of satisfactory shape was produceQ 9 was a Western Electric high­frequency loudf,peaker placed in a corner of the room and fed vvith 2 millise?ond pu:;'ses of 3 kcls tone. The output from an omnidirectional microphone placed in several positions in turn was fed to the standard oscilloscope fi~ted with a camera. The d:i.splays? of which }i'ig. 2 is a typical example 9 differ somewha t froIil those obtainerl wi th the mode} where there was very little overlapping of the separ",te echoes q the amplitudes of which could be indivic.ually measured. In Fig. 2 the "spikes" are in many cases ~he v0ctor sum o~ two or more echoes, and the displa~r therefore changez ra.pidly as the pulse length or the tone frequency is altered. The pulse irregularity values derived from these displays differ therefore from t~08e obtained with the flat model.

To meadure the irregularity the amplitudes of the individual "spikes" were measured and mu} tip lied by a factoL' of ""he form ekt , where k is a constant and t the time 9 thereby- compensating for the general exponential decay of amplitude. Two quantities were then calculated either being ci. measure of the irregularity or v3.:,:,iation of the amplitudes of the reflected pulses about the exponential

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curve. The quantity 0- is the standard deviation expressed as a percentaGe of the mean amplitude' while & is the mean actual deviation irrespective of sigYl 9 again expressed as a percent'age of the mean. 'l'he two quantities differ only in the weight which they attach to large variations from the general exponential envelope of the pulse decay and jt was found that the order that they assigned to different pulse decays was the samp.

'rIle first measurements on the effects of wall form were carried out in the experimental talks studio referred to above. Measurements of the frequenoy irregulari t;i*anc. pulse irregtllari t;'l were made with the studio in its original oOYldition and with the addition of 11 hemi­cylindrical plas -1;er castings 9 or 11 rectangv.lar castings fitted on the same posit:::. ons on the walls and ceiline. Fig. 3 shows the dimemdons of the two tJPes of diffuser. Existing castinGS were used and it will be seen that t1le volumes of the two types were comparable though not identica1 9 the rectanc,'Ulo"r diffusers being slightly the smaller. FiG. 4 S.tl.ows a typicZll arrangement of the diffusers as used in this and subsequent experiments.

Eighteen positions for the microDhone were u sed 9 threE:- l,eing in corners of the room, the others distributed over the floor and over the plane lyinG halfway betvveen the floor and the ceiling. The counter vas read at intervals of 100 c/s between 300 c/s and 1500 c/s and a Neumann level recorder was used in parallel with the analysing recorder to'provide a permanent record,

Very consideral11e vilria tions were found between the readings from different micl'ophone positions. No significant difference was found between the groups of ccrner~ floor and half-heigh"'; microphones~ and therefore no distinction was made between these groups in subsequent anahTis.

Examination of the results by statistical tests establishec. no significant difference bet'ween plain ''Valls? oylindrical diffusers or rectangu.ln.r diff'lsera 9 either as regards frequency or pulse irregu-· lari ty. r.rhe fR:;'lure of the experiment to show differences could be due to the fact that no differences existed, to ir.sensitivity of the method of measurement, or to the masking cf the effects by other factors. The clear indications given by the model experiments suggest3d that tho first two reasons did not apply, and it was concluded th'l t the condi tions of measurement in the :=;tudlO mupt be at fault. The most probable cause was the fact that the diffusers

JR; li'requency irregularity is the transmission irregularity for uni t frequency change.

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were mounted on a comparatively light inner wall and were therefore not acting as true boundaries to the sound field. ·These inner walls are constructed of G'J.ilding board and plasterboard panels of which the insulation is low, especially at low frequencies. It was possi [,le, in fact 9 t:) obtain from a microphone placed behind. this im!er wall a steady-·state record which was indis­tinguishable in general 8ppearanc~) from one ta~~en in the studio itself.

This sugeests tha,t it is incorrect to consider the room as being bounded_ bJ the inner walls. Variations in the shape of the inside wans will not directly sffect the sound field in the room, and the action of the diffusers may in fact be very comple~ because of their effect on .the "transparency" of the walls. With the. rectangular diffusers in place the walls and ceiling were more massive, and. the insulcdion at the high-:t'requency end of the ranee considered was probably higher.

In order to avoid e"~fects of this kind the experiment w'ts transfer:l'ed to the small reverberation room at Nightingale Square, a room with heu.vy rigid. walls.

IIoclified Procedure , _. -- -... --,~--- .. --",,,

ri'his room has a volume of 33 m~ (1000 ft 3 ) and is approxi­mately cubical; all the boundaries including the floor and ceiling are tiled. For the steady state meaDurements a B.T.H. "RK" speaker near and facing into a corner, was used a;3 a sound sourC0. An omnidirectional microphone, placed in several positlons in the room in ~urn, was t~e receiver.

To obtain th3 fre'luency irref;Ularity? tone fed to the loudspeaker v;as swept in frsquenc;y from 50 c/s to 1500 c/s a.t a rate of 8 m:'nutes per octave. The rb.te of sweep thus varied from 0.1 c/s per second belovv 100 Cif' tC' 2 c/s per second near 1500 c/s. Using Bolt's criterion we find that the maximum rate of sweep for steady state conditicns to be attained, is approximately 1 c/sper second at low frequencies and 4.5 0/8 per second at the high--frequency end of tl-:tn range. However? neither of the available level recorders was capable of following the rapid c~langes of level which occur at this rate of sweep~ and as it was not feasible to reduce the rat8 of swoop the automatic analyser could not be used.

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Instead j stead3T state records were obtained photographically using a standard logarithmic amplifier and oscilloscope. The output from the microphone was amplified by the logarithmic amplifier j

which produces a :D.C. output voltage proportional to the logarithm of the A.C. input voltage, and applied to the plates of the oscilloscope. The time-base of the oscilloscope was switched off and the spot set so that it moved vertically in the centre of the tube. A moving­film recording(c~mera, such as is normally u&ed for obtaining pulsed­glide displaJ!s' 8) 9 photoC;'Taphed the vertical movements of the spot. A steady state frequency characteris tic "vas obtained by gliding the film past the moving spot, the ordinates being proportional to level in decibels and the abscissae represen"ing frequency. Fig. 5 shows parts of three such records.

Me'asurements of the dif.2erence in decibels between adjacent peaks and dips on these records were made on an enlarged projected image of the photographic negative. The sum of these readings over a frequency baYld was divided b;y the difference in freql1ency between the beginning End end of the hand Cl,S before to give the frequency irregularity.

Five diffusers of the same typef as were '.~sed in the studio were mounted in the room' two of them were laid on the floor, the rest being fixed to three of the walls. The absorption introduced by the two types was almost identical over the frequency range considered.

J.1'ig~ 6 is a plot of the irregularity measured over the frequency range 50 to 1500 cls with the three conditions;-

A no diffusers B temi-cylindrical diffusers C rectangular diffusers.

It will be seen that the curves exhibit a broad maximum in the 200 cls to) 500 c/s region. SUch a peak vvas predicted by Bolt and Roop\.6 •

The results are summarised in the tables overleaf.

_. 10 -

Condition A B C ., .. -.. ~-.. --- .. ---------- ......... ---'" .... ,-,----~----- ' .. '_ .. __ ._._--_.-- .---..--.-. ..-.----Frequency RangEil

50 - 200 c/s 200 _. 800 c/s BOO - 1500 c/s

5·5 7·1 6.6

Microphone position

1 (corner') 2 (corner) 3 (centrA) 4

~J.~_ u _ ._. ___ ~_._ •••. _ •• ~~

7.1 6.B 7·0 6.5

__ .6.J ..

3.4 6.2 5.6

5.6 5. 2 5.6 5.2 5.7 5·1 5·5 4·9

.,5.· .6. ___ . 5.' L __

.. .9x...e•r.a)).. !l1.E_~!l ..•. ~. __ ~ .. _.,,§_.J_~ __ .. 2_~~ ___ 5_·.1. ..... ~ __ Approximate Standard Deviation 4~

It will be seen fro~ the table that the irregularity is least with the rect~ngu]ar diffusers and greatest with plain walls~ in every position and at. every frequency. If a correction for the reverberation time is made as described above? it is found that +'he change in irregu:'arity when hemicylindrical diffusers are introduced is no greater than that to be expected from the change in reverberati)n time. The substitution of rec~rmgu1ar diffusers for the hemi­cylindrical? however~ changes the irregularity significantl.y wi thou t a c or:ce sp~nding change of reverbera ti on time.

'1.'he variation in the irregularity with mic.:::,o-­phone position is very much smaller than in the studio, being about 2~0 comparod with about 107~

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in the Case of the experimental studio. uniform distribution of absorption of the probable reasons.

The smal:er volume and more reverberation room are the

For the measurement of pulse irregularity in the reverberation room the same method and equipment were used as for the studio. The table summarises the results.

Condition A ] C 6. __ ...... ___ ._~ __ ."""", ____ . __ ~~_._._,,"._"~~~. _. _______ .~__..._._. ____ ._ ...... __ .~". ___ ""' .. ___ ._

Microphone positiop

1 (corner) 2 (corner) 3 (co::011or) 4 (col.'nor) 5 (centre) 6 7 8

._9.

Hean

22 21 42 25 17 26 22 24

25

17 28 31 24 20 21 24

29 21 27 30 32 30 24 22

26

There isa marked variation in the value of O~ for different microphone positions? especially in condition A and the differences oetween the means are "lot sign~"ficant. It is interestin.; to note tha t the values of 0- a1',e aprreCiEl,b 1 y lower in this room than in the experimental studio; this may again be due to a more even distribution of absorption in the reverberatlon room.

The method of u\Jtaining pulsed-glide !'ecords in a room has been described elsewhere(2). ti record of ~his kind was obtained from the reverberation room in each condition and from these records were (9) derived values of tlJ.e quantity lilY' described in a previous report • This quantity is a meilsureof the variation of the envelope of the decay from a pure exponential form expres80d in decibels.

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J.i':blE3..,J_v:..~e_~_aL_~1~(3J0·~1_aE~ .. tLJpAe..!.~~~:.

_____ .. " __ ..9..~~"L t i op .. __ "_~ ____ ""_" ____ -,~~0.El.~_

A (No cliffusers) 3.6 B (H2mic;ylindrical (liffusers) 3.4 C (Rectant:,'Ulur dj}fusers) 2.6

~ifhereas th'3 frequency irregularity was found to increase in proportion to the reverberation time in a given room, the quantity liD" apJ:lears to cha'1ge very IJ1uch more slowly. Accurate tests are being made, and from the prel~minary results it is possible to say that the difference in "D" betY'leen condi.tions A and C is too large to be accoux,ted for by r~verbera tion time changes. The change betw"een conditions ,I\.. and B could be due to the latter cause alone.

The reducti.on of reverb'era tion time when the diffusers were put into the reverberation room may :1ave been 'partly due to absorption by the plaster cB-stings themselves? and partly to the increased_ efficiency of absorbing materials in a diffuse field. An experiment was therefore carried out in the leverberation room to find whether the presence of diffusors had any effect on the efficiency of absorbers in the room.

The reverberation time was moasured, using warbled tone at half-octave intervals from 62 c/s to 8 kC/s, with the room in four conditionsz-

l(a) (b)

2(a) (b)

Empty. With 54 sq.ft. of 1" deep porous soulld absorbing units Olly. With six hemicylindrical dLffusers only. With six hemicylin(~ri(~al diffuse:'s and 54 sq.ft. of 1" deep absorbers.

Care was taken that t:le extra absorbing material was not disturbod_ in any way" in Challging ';:'rom condition 1 (b) to condition 2 (b) 9 nOr the diffusers when changing :i.rom condition 2 (b) to condition 2(a). All the measurements ware completed within a few hours to reduce the possibility of-atmospheric changes affecting the absorbing material.

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The absorption of the matei:,ial at each frequency was calculated from two different sets of data!-

(1) From the difference in reverberation time between conditions lea) and l(b).

(2) From the difference in reverberation time between conditions 2(a) and 2(b).

'1'he two plots of absorption are shown in ]'igo 7. It will be seen that for frequencies above 700 c/s the absorption when diffusers were preLent was consistently higher than when there vvere no diffusers, tha increase being about 10%. Below 700 c/s the two curves can be considered as identical? but little change would have been expected below this frequency since the absorption is low. Low-frequency absorbers could not have been lr,troduced into the room as their depth woulu necessaril;r be sufficient to have some effect on the diffusion.

6. Conclusions

(a) 'l'h€ validi t~rof free-·field methods of assessing the effectiveness of different vlTall shapes in promoting diffusion is much in doubt.

(b) H'requency irregularity? pulse irre gulari ty end the dec,ay irregularity index may each be used as a measure of the diffusion in a room. A low value in each case indicatea go')d diffusion.

(c) All three of the above measures o~ diffusion are also affected by changes in reverberation time. In the case of frequency­irregularity? the value was proportional to reverberation time in the particular room investigated. (See also Appendix 2).

(d) The frequency irregularity va.::-ies considerably in different posi tiens in the room. It is necessary to take a mean of a large number of positions if small changes affecting the whole room are to be measu.£'ed.

(e) Shanges in wall shape in the experimental studio produced no significant differ(mce in the steady state or pulse irregularity. This is attributed to the fact that the diffusers were attached to thin inner vralls with very low sound insulation and it follows that the use of insufficiently rigid walls in the construction of a studio may invalidate the effect of diffusers.

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(f) TM.8 experiments in tho reverberation room showod a reduc:tion in the steady-state irregul(1,ri ty when rec'cangular diffusers were used. The hemicylindrical diffusers gave a smaller reduction which could have beon largely accounted for by the accompanyi~g r oduction of reverberation time.

(g) Tests of pulse irregu'arity in the reverberation room did not show significant differences betwe'm the wall shapes.

(h) J30th type.J of diffuser gave a reduction in the decay irre{!,ularity ind'3x~ the; rectangular being more effective.

(i) Above 700 c/~ the effective absorption coefficient of materials in a room is increased by the introduction of diffusers.

(j) Reviewing the experiments as a whole it is seen that Leveral were inconclusive? but that Il'hen a significant C1ifference 'v1Ta[, obt'1ined it confirmed the results of previous vrork9 namely that rectangular shapes are more efficient "tS diffusers than hemicylindricaL This result was obtained even though the rectangular shapes in these experiments had a smaller volume than the hemicylindrical. The present experiments suggest that the methods of short pulse analysis are not satisfactory for the investigation of diffusion in full-scale rooms. The most promising parameters are the frequency irregularity "Cnd the decay irre gu lari ty •

- 15 -

The (:ontact strip is iJ.escrioed in the te:;:t above and shown in Fig. 1. There are ~o contacts along the length of the strip, connected together in two grou:?s one of which consists of the 25 odd and the other of the 25 even contacts. The wiper arm is earthed J.nd the two groups are connected to the counter circuit as iJ.escribed below.

The c0unter circuit (Fig. 8) consists of four ECC 91 double triodes V2 ••• V5, the A and B halves of which are connected as R-C coupled multivibratorso These ,ilultivibrators divide incoming nega tive pulses into €,'TOUpS of 16 which are totalled by a mechanical counter in the anode circuit of V5. The simplest way to count the passage of the v:iper across a contact would be to connect a positive potential to the tvvo Groups of contacts so that earthing them would send a negative pulse to the anodes of V2 as in conventional counters. However, any noise or hllnting of the level recorder which caused the wiper arm to move on and off the edge of a contact wou1d send a series of triggering pulses and give a spurious coun-t. '1'0 overcome this, the +wo group::: of contacts are con~1ected to the two grids of a fifth ECC 91, V1, which is used as a D. C. amplifier, the grids being bia'3sed back when not earthedoy the wiper arm. Th9 anodes ol the valve are connected to the grids of the first multivibrator which therefore receive the triggering pulses instead of the anodes as in the normal arrangement. The action of earthing one grouD of contacts, say that connected'to the B grid of VI, causes a negative pulse to be transmitted from the anode to the B grid of V2, Assum1ng that the counter has been reset, V2' will change its sk,te 9 and no further uulses to the B grid will have any effect. If the wiper moves on to an "/\." contact however, the "A" gr:id of Y2,will receive a negative pulse and the multi­vibrator will count again. 'rhe circuit therefore counts only when the w:i.per moves from a contact of one group to one of the other. Positive pulses leave the anodes ef VI when the wiper moves off a contact but these positive pulses are prevented by the rectifier network in \72 W3 W4 from reaching V2. Without this network the trigc~ering action is critically dependent upon triggering voltage and may be unreliable in p:..~actic3.

- 16 -

Bol t and Roop (6 ) give the following formula, for the Frequency Irregularity in a room~-- [

2 . 401C V

Prequency IrreiJUlan ty ;j;' ·--~1 where V

V t c

If

volume of the room freque~1cy

wave coupling factor 9 usually about 1/8 veloci ty of sound in air frequenc~T spacing index (11)

aN= room absorption factor 9 becoming the absorption in Sab~nes in the limiting case.

, I Unfortunate]y, 'f can only be calculated for certain special

room shapes, but the formula can be used fo~ any given room to find the effect of cnangBs in absorption. In the experimental studio it implies that the irregularity is approximately proportional to the square of the absorption9 and somewhat less than th",s in the reverberation room. Thls result is not confirmed by tests made in the experimental studio described in this report.

In these tests the irregularity of the studio was measured without diffusers, extra absorption beine distributed as uniformly as possible over the walls for one of the measurements. The reverberation time curves for the two states are shown in Fig. 9 and the irregularity values ob-:aine~ are shown in table v below.

ittian ratio of reverberation time Ratio of irre@.llari ty

1.9 1.9

2.0 2.1

This tal)le shows that in the conditions of this ~xperiment the irregularity of the studio is proportional to its reverberation time.

- 17 -

References

(2)

(3) (4 )

(5)

(6)

(7 )

(8)

"Investiga tion of Sound Diffusion in Rooms by I'·iIeans of a ]lfodel" T. Somervi11e and F.L. Ward, "Acustica" 9 Vol. 1, No. 1, 1951 pp. 40 _. 48. "The Effect of Wall Sr"3.pe on the Scattering and Diffusion of Sound" Technical Memorandum ].1002, J.W. Head (Also in "Acustica" Vol. 3, No. 3 9 June 1953. ].8.661, definition 1210 (1936). "Standing-wave Patterns in Studio Acoustics", C.G. Mayo, "Acustica", Vo:. 2, No. 2, 1952, pp. 49 - 64. IIScha11ref1exion an FHl,chen mi t Periodischer Strclktur" E. JWeyer and 1. Bonn, "Akustische Beiheft" 4 (1952) pp. 195 - 207. "Frequency Response Fluctu'-',tions in Rooms", R. H. Bolt and R.W. Roop, J.A.S.~. Vol. 22, ~~rch 1950. "An Investlca tion of Small Talks Studios", Research Heport B, 047 (19'11). "Cathoc'e-Hay Displays of Acoustic Phenomena and their Interpreta­tion" Hesoarch Report B.046, T. Somerville and C.L.S. Gilford (Also in B.B.C. (,~uarterlY9 VoL VII, No. 1, 1952, pp. 1 - 13. !'An Empirical Acoustic Cri tericn" Research Report ].053 (1953) '1'. Somervillo (Also in publication in "Acustica").

ISSUE 1

21-10-53

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(c) R~ctangular diffus~rs

Fig.5 Typical photographic displays of steady-stat~ charact(ristics

300

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