An improved geometrical sound field analysis in rooms using scattered sound and an audible room acoustic simulator

Applied Acoustics 38 (1993) 115-129

r

. . . .

An Improved Geometrical Sound Field Analysis in Rooms Using Scattered Sound and an Audible Room Acoustic Simulator

Kiyoshi Nakagawa, Toru Miyajima & Yasuhiko Tahara Institute of Technology, Shimizu Corporation, 3-4-17 Etchujima kotoku, Tokyo 135, Japan (Received 2 December 1991; revised version received and accepted 13 March 1992)

A BSTRA CT A geometrical computer simulation model and an audible room acoustic simulator, based on ray tracing with scattering effects, are presented. This calculation model classifies the receiving sound energy into three O'pes. Direct sound energy is calculated with the inverse square law, and early reflected and d(ff'use sound energy are calculated with the effective geometrical reflection energy coefficient using a simple diffraction theory for a.finite free reflecting panel. Two actual halls are used to compare measured and computed values o f .['our acoustic parameters: Clarity (C), deutlichkeit (D), lateral efficiency ( L E ), and room response ( R R ). It has been found that the new calculation model is a better evaluator of C, D and R R than the traditional ray tracing method. The room acoustic simulator has been used to simulate sound in the halls using 15 channels. The simulator can judge acoustic hnpressions in the presence of reverberation, clarity and spaciousness.

1 INTRODUCTION Computer simulation is a room acoustic design tool very useful in predicting sound propagation and obtaining acoustical information in the design process. At present, computer simulations based on geometrical acoustics are particularly in widespread use. 1 -4 By using geometrical acoustics such as the ray tracing method (RT method) or the image source method (IS 115 Applied Acoustics 0003-682X/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain

116

Kit'oshi Nakagawa, Toru Mi),a/ima, Yasuhiko Tahara

method), it is possible to obtain the approximate impulse response and the objective parameter in a short time. However, errors can sometimes occur depending on the complexity of the diffraction or the diffusion, and the excessive reflection sound energy which occurs when the wall size is small compared with the wavelength. To improve such predictions, some models incorporating diffuse reflections have been proposed. 5"6 The objective of this paper is to examine a new geometrical acoustic model considering the scattered sound (RTS method) 7 and the room acoustic simulator based on the RTS method. In the following, an outline of the RTS model is first described as an extension of the RT method. The reflection sound is defined by two sound components: the geometrical reflection sound and the scattered sound. The geometrical reflection energy is calculated using the geometrical reflection coefficient derived from the simplified diffraction theory for a finite free reflecting panel, s The difference between the total reflection energy and the geometrical reflection energy, is assumed to be the scattered sound. Effectiveness of the new model, complete with examples of applications to actual halls, is also shown. In addition, the audible simulation system based on the RTS method and some experimental results are described. 2 RTS M O D E L 2.1 General description of the new model In the original RT method, sound energy at the observation point It, is expressed as follows: W x Ni, [ I

I,.

S-s

I I (1 -

(1)

k=l

where Wis the sound power, N is the total number of sound rays emitted by the omnidirectional source, Ni, is the total number of received sound rays, ~t is the absorption coefficient of the reflecting wall. AS is the area of the receiving zone, n is the number of reflecting walls hit by the sound particle and k is the running wall number. If N is large enough and AS is appropriate, the calculated value of It, will be approximately the same as the value obtained by the IS method. Figure 1 shows the sound propagation of the RTS modelfl The geometrical reflection energy coefficient J ( 0 _ J < 1) is then assumed for calculating the reflection sound. J is defined as the ratio of the sound energy reflected from the square wall to that reflected from the infinite rigid wall,

Simulation o1"room acoustics using geometrical scattering sound

geometrical reflected m l h .,ill~ J4 ( l - a e s ) • W / N

(1 i &

[ ineidlmt W/N

'=

)(1-or.

" W/N

: ~

117

roll,

//

I,

omidirectional

Fig. 1. Sound propagation model using diffuse sound. 14/is the sound power, N is the total number of rays emitted by the omnidirectional source, Jk is the geometrical reflection coefficient of wall k, and ~k is the sound absorption coefficient of wall k.

and is calculated from the simple diffraction equation. 8 Thus, J is obtained from the following expression with a function of frequency:

j,~,

s~ 11

1) 2

+70_ cos20,.

¢21

w h e r e f i s the frequency, S~ is the wall area, 0~, is the incident and reflecting angles at which the sound arrives at the wall, 2(./") is the wavelength of incident sound, s o is the distance between the source and the reflecting point, and r o is the distance between the reflecting point and the observation point. Ifeqn (2) gives a value of J(f) greater than 1, J(f) is set at 1 in order to fulfil 0 < J < 1. In the case of multiple reflections, the distance between the previous reflecting point and the present reflecting point is assigned to So, and the distance between the present reflecting point and the next reflecting point is assigned to r 0. The total energy factor is calculated by multiplying J(f) obtained from each reflection. An experiment using square acrylic panels was done to estimate the effectiveness of J(f). Figure 2 shows the disposition of panels, source points and observation points, in which the incident and reflecting angles are arranged at 45 °. Figure 3 shows the comparison of reflection response between the measured and the calculated values. In cases of single and double reflections, the calculated values are in good agreement with the experimental values. From the comparison of this data, it seems that J(f) provides fairly good predictions for the geometrical sound energy. In the case of the multiple reflections or the narrow wall, geometrical reflection energy by using J(f) may be calculated less than the measured reflection energy.

I 18

Kiroshi Nakagawa, Toru M(ra/ima, Yasuhiko Tahara

Rz

"<"J J l ~,~

J

~-~

1"i u~'/I

45"

~

~1~

l ["'-.I/"la

1.0 m J'4s.

"

SP Fig. 2. Disposition of the sound source and observation points for the experiments and calculation. SP is the source point, O, and O2 are geometricalreflectingpoints, R, and R 2 are observation points.

After the reflection off the wall, the geometrical reflection energy, given as W Ik = ~ x (1 - ~)Jk

I k,

is

(3)

where, k is the running wall number. The difference between total reflection energy and the geometrical (JB) 20

I

,

t

iI

~.--

l

i

i

I

I

J

I

II

Calculated by lormula (2.)

tsi,X,,rm,cuo,l / - ) ~ . ~ y ' R I ~

-1o

II V I

-20

~ -30 I

500

I

I

I I (

lk

I

i

t

I

i

2k 5k Frequency (Hz)

i

,

tl

10k

20k

Fig. 3. Comparison of reflectionresponse between calculated and measured values. 0 dB is the reflected sound level from the infinite reflecting panel.

Simulation of room acoustics using geometrical scattering sound

I 19

reflection energy is then assumed to be the scattered sound energy. Total scattered energy I, is given as I, = W x (1 --

~tkX1

-

1¥

Jk)

(4)

2.2 Formulation of the model Figure 4 shows the idealized sound energy decay obtained by the RTS model at the observation point. The scattered sound is assumed to propagate omnidirectionally and to decay with the exponential law. The following three different sound components are then calculated. Direct sound

(5)

W × Nin Id= A S x N Geometrical reflection sound

In(f)=

W x Nin ~2] (1 - ~k(f)) X Jk(]') ASN

(6)

k=l

Scattered sound I~c(.f)

-- ~

1

I,(.f)

(t = t~c + td~)

--ksc(f) x e x p -

1 • t - tsc\ 38T--~)

(7a) (t>t~c+td~)(7b)

where It(f) is the total scattered sound energy offthe reflection wall, rc is the Direct sound ;eometrical reflections

Fig. 4.

Time Received sound decay by the RTS method. Thc cross-hatching represents the scattered part.

K(voshi Nakagawa, Toru Miyajima, Yasuhiko Tahara

120

wall-to-observation point distance, T(f) is the reverberation time, ts¢ is the time taken to travel from the source to the reflecting point, and tds is the time taken to travel from the reflecting to the observation point, ksc(J" ) is the energy constant according to eqn (8), which assumes that the first reflected scattered energy is distributed with exponential decay in the time corresponding to the mean free path (= 4 V/S). 4It(f X1 -- ~(f))/S k~c(f) - ('4v/¢s [ - 13-8t\ exp~ ] v - ~ - ) d t

(8)

Jo

where ~(J') is the average sound absorption coefficient in the room, V is the room volume, S is the room surface area and ¢ is the sound velocity.

2.3 Comparisons of RT and RTS predictions for actual halls The RT method and RTS model were applied to auditoriums to examine the practicality of the simulation model by comparing the correlation and the

z

Z

Y-LFig. 5.

(b) Hall's configuration of the computer model. (a) K hall, V= 1600 m 3, T (500 Hz)= l'04s. (b) S hall, V=4910m 3, T(500Hz)= l'2s.

Simulation o f room acoustics using geometrical scattering sound

121

tendency between the calculated results and measured results. For both computer simulations, 40 000 sound rays were emitted and calculated up to 500ms with the seats reflection ignored in the RT method. For the measurements, tone-burst signals radiated from an omnidirectional loudspeakers (TS-1) 9 were used. The tone-burst signals were generated by applying a Hanning window over all six sinusoidal waves. The sound signals were received by a microphone (AKG C422 comb) located at a measuring point, of which both the omnidirectional and the figure-eight directional patterns were used. Figure 5 shows the configurations of the two auditoriums. One is the 'K' lecture room, the other is the 'S' multipurpose auditorium. Table 1 shows the computer room conditions compared with the real auditorium conditions. In order to examine the new model, the following four acoustic parameters were used: clarity (C) and deutlichkeit (D) which relate to the reverberation or the clarity, lateral efficiency (LE) and room response (RR) which relate to the spaciousness. Figure 6 shows the echo time pattern of the measurements and the Measured

RT method

100ms

Fig. 6.

Comparison of echo time pattern between measured and calculated value. (K hall, ! kHz, centre seat).

122

Ko,oshi Nakagawa, Toru Mo'ajima, Yasuhiko Tahara

6

e., e.q

tl

~z

e~ tl

zz E te~ 0

t~ ,d

0

E etO e~

time

e~

E 0

e~

8 O

i

e~

e~ e-

Simulation

o/" room acoustics using geometrical scattering sound

123

(dB)

I0

//

3

//.' ~*

5

I00

~40 -

r:

RTS m e t h o d

r= 0.770 7' m e t h o d r = - - 0 . 1 2 9 ,

0.865

value

1.0

o',io

10

2dB)

1".1=:-

'-~

Rrmethod 0

,

0

,

0.2

t

.

Rrs..th.d ,=0.an ,

0.4

,

,

0.6

,

" ,

0.8

Measured value

,

i

1.0

8

ioo

"..*.*~" ~*/

/

,=0.406

80

1::~ R.

0

e-2

"*

eo

Measured value

.~1~~

0.8 ~o.e

E)

.

''

~**~ RTS method Measured

C

RrSme,ho~ ,=

/

~r

o.53s

RTmethodr=-O.143

(dS)

,

-8

--6

-4

-2

0

2

Measured value

Fig. 7. Comparison between measured and calculated values of acoustic parameters. RTS method: S hall (-k) I kHz, K hall (A) 500 Hz,(O) i kHz,(m) 2 kHz,(O)4 kHz. RT method: S hall (~r) 1 kHz, K hall (A) 500 Hz, (O) 1 kHz, (I-1) 2kHz, and (~) 4kHz.

simulation. The calculated patterns are the results showing the impulse responses convolving with the sound waveform. When comparing with the measured pattern, it was found that the echo time pattern obtained by the RTS model had similar reflection energy dependent on the wall size, and a smooth envelope in multiple reflections. However, the echo time pattern obtained by the RT model, did not correspond to the measured pattern. Figure 7 shows the comparisons of the measurements and the simulation. The results are as follows: (1)

Comparing the correlation coefficient, the values of C, D and RR obtained by the RTS model are higher than those by the RT model, and the value of C by the RTS model is the highest standing at 0.865. (2) Comparing to the measured values, the absolute values of C as well as D obtained by the RTS model, are lower than the measured values,

Kivoshi Nakagawa, Toru Mivajima, Yasuhiko Tahara

124

however, the general trend of C is in good agreement with the measured values. (3) With the RT method, the errors are large, and the tendencies of C, D and RR do not correspond to the measured values. (4) The differences of the LE values of the correlation coefficient, as well as the tendency between the RTS model and the RT method, are not found. From the comparisons of this data, it was found that the RTS model seems to be a fairly good predictor of C, D and LE. 3 AUDIBLE ROOM ACOUSTIC SIMULATOR BASED ON THE RTS MODEL 3.1 Simulated sound components The room acoustic simulator produces four sound components: the direct sound, the early reflections, the reverberation, and the scattered sound. 9'1° Figure 8 shows the idealized sound decay pattern obtained by the room acoustic simulator. The early reflections are simulated according to three parameters: the time it takes to reach the listener, the sound pressure level, and the direction of the sound. All early reflection data are classified into 15 spatial directions, and are computed up to 304 reflections. The scattered sound has been simulated into two components: the frontal sound and the back sound. The reverberation has been simulated assuming an exponential sound decay process in a diffusing room. 3.2 Hardware of the room acoustic simulator Figure 9 shows the system diagram of the room acoustic simulator for sound effects in an anechoic room where 15 loudspeakers are placed. All of

m

oo

T i m e ( ms ) Fig. 8.

Produced sound c o m p o n e n t by the r o o m acoustic simulator.

Simulation of room acoustics using geometrical scattering sound

Direct Early

125

sound reflection

w I

• J lhl,,

:1

'-

~'-_~= q

~t

]

[q ~ A n e c h o i c r o o m

Q'

LTi

IPl|

o

Dry r- ~ Suuroe

~ IIh

~t

~

~.

VERTICAL

B

Risht

~

Scattered sound ,tlllht,,,.

;t

I

~

Computer

'-

o.,,-"-- 111

:

Front

;ack

B

'

Reverberat ion

SP? I

[eft

HORIZONTAL

~ M I O I (to Effecter end Digital Equellzer) >R S 2 $ 2 C (to leverberator and I l x t r l x H l x o r )

Fig. 9.

System diagram of the r o o m acoustic simulator.

these loudspeakers are arranged at an equal distance (2 m) from a listening position. Eight of them are arranged in the horizontal plane and others are arranged above them. 11 The direct sound is produced by the front loudspeaker (SP1), the scattered sound is produced by the four lateral loudspeakers (SP2 and SP8, SP4 and SP6) and the reverberation is produced by the upper four loudspeakers (SP10, SPll, SP13 and SP14). Using the RTS procedure, it is possible to determine the sound pressure levels and the delay times of each directional impulse response for each octave (63-8 kHz bands). Each directional impulse response is computed in the frequency range of 160 Hz to 4 kHz. In order to convert these data into the room impulse response, the input signals, such as impulse or anechoic signal must be properly delayed and attenuated by hardware. The following equipment is used for this purpose: a digital equalizer (Yamaha DEQ7), a digital delay unit (Yamaha YDD-2600, SPX1000) and a

126

Kivoshi Nakagawa, Toru M~vqjima, Yasuhiko Tahara

I

~A

,..,--¢'qC'q,...~--

e-~

e.. 0

~ 6 ~ 6 6 E 0 o e~ ¢'qt",l~-I~-e,q

E 0 r~ r~

0 e.

e.. 0

dT~

E 0 0

¢'q

t'q

e.,

e. 0

e~ e-

-

= <

Simulation o.f room acoustics using geometrical scattering sound

127

digital reverberator (Yamaha REV1). In the experiments, the direct sound, the early reflections, and the diffuse sound were calculated directly up to 250 or 315 ms. The reverberation was calculated using the theory of reverberant sound fields. 3.3 Application of the room acoustic simulator The room acoustic simulator was applied to three different actual rooms: an auditorium having a volume of 2887m a, another auditorium having a volume of3217 m a, and a gymnasium having a volume of 19 430 m 3. Table 2 shows the computer room conditions compared with those of the real halls. In order to evaluate the room acoustic simulator, subjective judgement and the correlation of the following four acoustic parameters were used: C, D, RR, and the modulation transfer index (MTI) which relates to the intelligibility. For the judgement of subjective similarities between the real and the simulated fields, three short-duration music pieces by a piano, flute, and a female vocalist as well as by male speech were recorded in the two fields 100

(dB)

(%)

C

I3>

=~80

o

~ o

~ 40 a

-55

2

' ' 0 ' Real field value

5(dB)

00

(dB)

i

,

i

f

l

l

l

l

1.0

R R

, (%) lOO

l

40 ~ Real field value

N/IT

I

== >-

q=,

o

"..-º; - 2

¢,.

"0.5

-4 S

~-6 -8

• (dR)

-6

-4

-2

Real field value

0

2

0.0

0.0

Y l

l

l

,

=

,

l

,

l

0.5 Real field value

r

1.0

Fig. 10. Comparison between acoustic parameters in real field and those in simulated field. F hall ( 0 ) 1 kHz, U hall (C)) I kHz, M gymnasium (&) 500Hz, (A) I kHz, ( 1 ) 2kHz, (FI) 4 IHz.

128

Kiyoshi Nakagawa, Toru Miyajima, Yasuhiko Tahara

using a dummy head microphone (KOKEN ORA-1B). These recordings were later replayed to five people through headphones. The subjective impression were as follows: subjective spaciousness and reverberation were in fairly good agreement. However, the subjective position of the simulated source was nearer than that in the real room, and in the case of speech, or sound with long reverberation time, it was found that the colouration depended on the reverberator. Figure l0 shows the results of the comparison between the real and the simulated sound fields. The correlation of C, D, and MTI values obtained by the simulated fields, when compared to the real field values, are accurate. However, the correlation of the R R values is low, which is dependent on the probability by the RTS model. It seems then, that the proposed room acoustic simulator can judge reverberation, clarity and spaciousness. A subject test to evaluate in detail the similarities between the real and the simulated fields is in progress.

4 CONCLUSIONS (1) An improved geometrical calculating model (RTS model), based on the original RT model and incorporating diffuse sound, is described. Some examples of applications for actual halls are shown. The comparison of the acoustic parameters indicates that the proposed RTS model is useful and can predict the approximate acoustic parameters of C, D and LE. (2) Based on the RTS model, a room acoustic simulator has been developed. Comparison between the real and the simulated fields, using subjective impressions and acoustic parameters shows that the proposed room acoustic simulator can judge acoustic impressions in the presence of reverberation, clarity and spaciousness. Some problems which require further improvement, such as incorporating the seats' reflectivity, remain in the present RTS model. Nevertheless, the RTS model and the room acoustic simulator are useful for room acoustic design and can judge acoustic impressions in halls.

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Simulation of room acoustics using geometrical scattering sound

4. 5. 6. 7. 8. 9. 10.

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129

Acoustical Design of a Room and Problems. Research Data, Architectural Acoustics Committee of Acoust. Soc. Jpn (in Japanese), Acoustic Materials Association of Japan, Tokyo, Japan, 1982, AA82-35. Strum, S., Dahl, H., Krokstad, A . & Eknes, E., Acoustical design of the Grieg Memorial Hall in Bergen. Appl. Acoust., 18 (1985) 127-42. Kuttruff, H. & Stral3en, Th., Zur Abh/ingigkeit des Raumnachhails vonder Wanddifusit~it und von der Raumform. Acustica, 45 (1980) 246-55. Von Rietshote, H. F. & Houtgast, T., Predicting speech intelligibility in rooms from the modulation transfer function V: The merits of the ray-tracing model versus general room acoustics. Acustica, 53 (1983) 72-8. Nakagawa, K., Evaluation of room acoustic indices by an improved geometrical sound field analysis with scattering phenomenon. J. Acoust. Soc. Jpn (in Japanese), 45(12) (1989) 934-41. Yamamoto, T., Reflection characteristics of diffusing walls. In Proceedings of the 6th International Congress on Acoustics, Acoustic Materials Association of Japan, Tokyo, Japan, 1968, E-l-7. Tachibana, H., Yano, H. & Kaite, M., Room acoustic measurements by using a dodecahedral loudspeaker system. Technical Report of the Electrical Acoustics Committee of the Inst. EICE. Jpn (in Japanese), 1988, EA88-3, pp. 13-18. Tahara, Y., Miyajima, T. & Nakagawa, K., Alternative approaches for audible room acoustics simulator based on the geometrical sound theory. In Proceedings of the ASJ Annual Meeting of Acoust. Soc. Jpn (in Japanese), Acoustic Materials Association of Japan, Tokyo, Japan, pp. 661-2. Miyajima, T., Tahara, Y. & Nakagawa, K., Audible room acoustics simulator with scattered sound. In Proceedings of the ASJ Annual Meeting of Acoust. Soc. Jpn (in Japanese), Acoustic Materials Association of Japan, Tokyo, Japan, pp. 663-4.