1969 measurement of sound diffusion in small rooms

8/6/2019 1969 Measurement of Sound Diffusion in Small Rooms

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UDC 534.84

~B. ( ! I i'rHIO:CIJr.E:~1I " .....~AOTO I .! ! IOu IT I llYRESEARCH DEPARTMENT REPORT

The m easu rem en t o f sound d iffus ioni n d e x i n s m a l l r o o m s

N o . 1 9 8 9 / 1 8

Research Department, Engineering DivisionTHE BRITISH BROADCASTING CORPORATION


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RESEARCH DEPARTMENT

THE MEASUREMENT OF SOUND DI FFUSION INDEX IN SMALL ROOMS

N.F. Spring, B.Sc., A.lnst.P.K .E . R an da ll, A ss oc ia te Member I.E.E.(PH-32~

Research Department Report No 1969/16UDC 534.84

This Report may not be reproduced in anyform without the written permission 01 theBritish Broadcasting Corp oro t ion ,It uses SI units in accordance with B.S.document PD 5686.

Head of Research Department


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Section

!PH-32)

Research Department Report No. 1969/16

THE MEASUREMENT OF SOUND DIFFUSION INDEX IN SMALL ROOMS

Title

SUMMARY __ __ . _. __ __ _. .. .

1. INTRODUCTION _ _.. _. _ __

2 . EXPERIMENTAL PLAN . _ . . _ _

3. THE SIX STATES OF THE ROOM - - .. - - - .

4. THE MEASUREMENTS __ __ _ _ - .4.1. Variation of Reverberation Time with Position .. _ .. _ __ . . 24.2. Curvature of Decays _ _ __ . _ .. __ . __ . _ _ . . 24_3. Directional Microphone Measurements _ _ . . . . 4

5 . SIGNIFICANCE OF THE RESULTS

6. CONCLUSIONS AND RECOMMENDATIONS

7 . REFERENCES __ _ __ _ __ .

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July 1969 Research Department Report No. 1969/16UDC 534.84

THE MEASUREMENT OF SOUND DIFFUSION INDEX IN SMALL ROOMS

SUMMARYThree methods of measuring sound diffusion are described. One is derivedfrom the curvature of sound decay curves and a second is based upon the variation ofreverberation time with position. Both these yield useful indices of diffusion and aresuitable for automatic analysis with the aid of a computer. A third method, using arotating directional microphone, was found to be valueless for small rooms of moderate

absorption, although it is reported to yield a useful index for large or very reverberantrooms.

1. INTRODUCTIONA sound fie ld is sa id to be diffuse if:(a] there is uniform sound energy density within the

region considered, and(b I there is equal mean energy flow in all directions at

any point in the field.In the derivation of reverberation-time formulae, a

diffuse sound field is assumed and sound absorption co-efficients must, strictly, be measured in a reverberationroom in which the sound field is diffuse, However, currentinterest in diffusion measurement does not arise only fromConcern about the theoretical basis of reverberation timeand the accurate measurement of absorption coefficients.The main reason is that certain acoustical defects in a room,e.q, flutter echoes, are associated with concentrations ofsound energy in specific directions and that such defectscan be cured by taking steps to scatter the energy moreuniformly_

Even now, reverberation-time and its variation withfrequency are the only widely accepted objective criteriafor the quality of a room; they are also widely recognizedas necessary but not sufficlent criteria, It has often beenremarked that two rooms having the same reverberation-time/frequency characteristic can sound surprisingly dif-ferent; the determination of an index characterising thestate of diffusion of the sound field in a room appears to bethe next and, perhaps, the final step in establishing satis-factory objective criteria.

There are two difficulties about basing measurementtechniques on the definition of diffusion.

The fi rst, a practical one, is that means of measuringsound energy and sound energy flow are not generallyavailable. Microphones respond to sound pressure, soundpressure-gradient or a Iinear combination of these. Whilethere are simple relations between sound pressure and energydensity for the fields due to plane and spherical waves, ingeneral no definite relations exist tor the types of non-diffuse sound field found in rooms, The second difficulty,a theoretical one, arises from the fact that only the ideal

(PH-32)

state of perfect diffusion is defined quantitatively.Departures from the state of perfect diffusion can arise

from inhomogeneity in the sound energy density and fromanisotropic energy flow, so that a true measure of diffusionmight involve two independent parameters, It is not sur-prising that most investigations into the measurement ofsound diffusion have been based on empirical approaches,using parameters related only indirectly to the basic attri-butes of a diffuse field. Most of these parameters areunsatisfactory measures of diffusion in practice eitherbecause they are difficult to evaluate or because they aretoo insensitive. Others are applicable only to large roomsand are of limited value to a broadcasting authority having alarge number of talks, interview and discussion studios,

A practical study of sound diffusion in small roomswas made by Randall and Ward. 1 They varied the surfacedistribution of absorbents and also used a nu mber of dis-posable solid shapes which were attached to the walls andfloor to scatter the sound on reflection. Parameters indi-cating the state of diffusion were derived by examiningcertain characteristics of the reverberation decay-curves.Useful though these parameters Were, the time taken toevaluate them discouraged their general use, However, withthe development of automatic reverberation time measu re-ment,2 it was decided to investigate whether indices of dif-fusion based on the work of Randall and Ward could beobtained automatically from the digital decay data onpunched paper tape. Two parameters appeared promising:-

(i) P, a quantity representing the variation of slopeof the decay curves with microphone position,was the standard deviation of the reverberationtime, obtained from warble tone pulses,


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22. EXPERIMENTAL PLAN

Randall and Ward showed that the state of diffusioncould be controlled by a suitable distribution of absorbentsover the surfaces of the room. Six different arrangementsof absorbers were set up, in the experimental studio, which,from past experience, wou Id be expected to cover the rangeof states of diffusion encountered in broadcasting practice.For each room condition, digital decay data on punchedpaper tape were obtained from the test recordings used inautomatic reverberation time rneasurernent.f With suitableprogramming the paper tapes were then processed in a corn-puter to yield parameters closely associated with P and S.

In view of the complicated nature of diffusion itseemed likely that the two new computer-derived indiceswould not, at best, give precisely the same rank order forthe six states of the room. At worst, they might not becapable of distinguishing the states of the room at all. As acheck, it was decided to assess the states of the room by anindependent method involving the use of a directionalmicrophone.

3. THE SIX STATES OF THE ROOMThe experimental studio has the dimensions 87m x

4gm x 34m. The six different distributions of absorbentsare shown in Fig. 1; for all conditions other than F therewas a woo Icord carpet with underfelt covering the floor.The absorbent surfaces consisted of a combination of low-frequency, mid-frequency and high-frequency absorbers inmodular sections, of dimensions 122m x 061 m, distributedevenly over each surface.

D E F{no corpet}Fig. 1 - Distribution of absorbents for the six states of theexperimental studio

~ Absorbent surfece 0Reflecting surfaceThe reverberation-time/frequencv curve for each con-

dition is shown in Fig. 2. Condition A would be acceptablefor broadcasting purposes.

The ten microphone positions for the reverberation-time measurements, and hence for the modified P and Sdeterminations, are shown in Fig. 3. The loudspeaker was aBBC Type LS5/5, pointed into a corner to reduce the levelof the direct sound. An omnidirectional microphone wasused.4. THE MEASUREMENTS

4.1. Variation of Reverberation Time with PositionThe computer printouts of reverberation time for the

six conditions enabled the standard deviation of reverbera

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63 125 250 500 1.000 2POO 4,000 Bj:O o

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aFig. 2 Reverberation times of experimental studio

(a)o--o Condition A (dl.6--_4 Condition 0IhIX---x Condition BIe 1.- -. Condition C (elo ._ .._o Condition E([14. __ ..._.... Condition F

tion time at each frequency to be derived. When expressedas a percentage of the mean reverberation-time this gave theindex P c, closely related to Randall and Ward's P . P c wasobtained with 1/3 octave-bandwidth noise-excitation from50 Hz to 8 kHz, at ten microphone positions, in contrast toP which was obtained with warble-tone excitation from500 Hz to 8 kHz at fifteen positions.

The variations of P c with frequency, for the differentroom conditions, are shown in Fig. 4.

Since the variation of P c below 1 kHz appeared essen-tially random, the mean P c for the 1/3 octave-bands be-tween 1 kHz and 8 kHz was calculated for each conditionand the results are shown in Table 1.

TABLE 1Room Condition C

16 8D24

E F7

A B35

4.2. Curvature of DecaysFirst attempts to programme the computer to extract

the index S from reverberation test-tape data producedabsurd results. This arose from the difficulty of construc-ting an algorithm by which the 'upper halt' and 'lower half'of a decay curve could be recognized. By dividing thedynamic range into two halves and programming the com-puter to run down the decay until the half-way level wasexceeded, it was hoped that the mean reverberationtimeabove this point divided by the mean reverberation-timebelow, would yield the index S. Unfortunately, decaycurves Iike that shown in Fig. 5 gave answers that wereclearly wrong.


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o 63 250 500 \000 2.000 4,000 aoooIrtt(fucmcy, HzFig. 4 - Variation of reverberation time with position, Pc(alo---o Condition A (dlA lI. Ccndition0(b)(---X Condition B (elo---CI Condition E(c).-_. Condition C (f)~--.- ...~ Condition F t",,,,.Fig, 5 -A nomalous measurement of S


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4

Modifications to the definition of S were tried butthey generally gave unreasonable answers with particulartypes of decay curve; that is, the indices derived were un-satisfactory because they were unduly sensitive to minorand acoustically unimportant characteristics of the decaycurves.

Fortunately, one modification to S was found to besatisfactory in this respect. The computer was programmedto construct a line passing through the commencement ofthe decay curve (point A in Fig. 6), with a slope equal tothe mean slope of the decay down to 6 dB above the noiselevel lpoint B in Fig. 6). The ratio of the area boundedby the real decay curve AB and the lines AC and BC, to thearea of the triangle ABC was taken as a rneasu re of thecurvature of the decay curve. The resulting index, calledSA' was found to give results free from serious anomalies,presumably because minor characteristics of the curve makeonly a small contribution to the area under the curve.

The data used for deriving SA was the same as thatused for Pc'

. -~. ..L~"".5 1

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Fig. 6 -Measurement ol SA

It should be borne in mind that S differs from SA in anumber of ways: S was measured with pure tones and theresults were averaged over twentv-stx tone- b ursts at 2 Hzintervals covering a band 25 Hz above and below the fre-quency of interest and at only one position in the centre ofthe room, whereas SA was measured with noise of one-third-octave bandwidth at ten positions in the room. Whenever an individual reading of S exceeded unity the reciprocalof S was used in forming the mean of a set of readings, onthe grounds that otherwise a set of convex and concavecurvatures would tend to an average of unity. This pro-cedure was not followed in the determination of SA becauseit was felt that there is a greater danger that random errorsin the measurement of SA for a set of essentially straightdecay curves would thereby be converted to systematicerrors reducing the value of SA to less than unity.

The results of the measurements of SA in the experi-mental studio are shown in Fig. 7. As with PCI there islittle to distinguish the curves below 1 kHz. The mean SAfrom 1 kHz to 8 kHz for each room condition is shown inTable 2.TABLE 2

Room Condition B D E Fc0'93 085 080 0'87 0'89 096

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1969 measurement of sound diffusion in small rooms

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