Acoustic Design of a Reverberation Chamber

8/11/2019 Acoustic Design of a Reverberation Chamber

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Applied Acoustics32 ( 1991) 83-91

coust ic Design of a Reverberat ion Chamber

Xiang Duanqi, Wang Zheng Chen Jinjing

A c o u s t i c La bor atory , Beij ing Insti tute o f Architectural D esign and Research,

Beijing 100045, People 's Repu blic of C hina

R e c e i v e d

I F ebr ua ry 1990: accepted 5 April 1990)

ABSTRACT

It is of great importance in acoustic design to establish a diffuse sound field in

a reverberation chamber. Though various attempts have been made to

establish sound diffusion in most existing ret erberation chambers, the results

were not good enough, and consequently extra diffusers have had to be

installed. Excellent sound diffusion has been obtained in the reverberation

chamber to be discussed in this paper by using an irregular shape and tilted

walls with fixed reinforced concrete spherical diffusers. In this paper the

authors have emphasized the design of sound diffusion and also discussed the

design and determination of the acoustic properties of the reverberation

chamber.

1 I N T R O D U C T I O N

T h e A c o u s t i c L a b o r a t o ry o f H a n g z h o u E l e c t r is o u n d F a c to r y s i t u a te d in

H a n g z h o u C it y t h e c a p i ta l o f Z h e j i a n g P r o v i n c e C h i n a c o m p r i s e s t w o

p a r ts a n a n e c h o i c c h a m b e r i n t r o d u c e d in a n o t h e r p a p e r ~ a n d a

r e v e r b e r a t i o n c h a m b e r t o b e d i s c u s s e d h e r e i n d e t a i l . T h i s r e v e r b e r a t i o n

c h a m b e r i s b u il t t o m e a s u r e t h e p e r f o r m a n c e o f l o u d s p e a k e r s a n d

m i c r o p h o n e s i n a d if fu s e s o u n d f ie ld t he s o u n d p o w e r l e v el o f l o u d s p e a k e r s

a n d o t h e r s o u n d s o u rc e s a n d a b s o r p t i o n c o e f f ic i e n t o f m a t e r ia l s f o r w h i c h

p e r f e c t s o u n d d i ff u s io n l o n g r e v e r b e r a t i o n t i m e u n i f o r m s o u n d fi el d

d i s t r i b u t io n a n d l o w b a c k g r o u n d n o i s e l e v e l a r e r e q u i re d . T h e r e f o r e t h e

d e s i g n s h o u l d m e e t t h e f o l l o w i n g r e q u i r e m e n t s .

83

Applied Acoustics 0003-682X/91/ 03-50 1991 E l s e v i er S c i e n c e Publishers Ltd, En gland .

Pr in ted in Grea t Br i ta in


2/9

84 Xiang Duanqi Wang Zheng. Chen Jinling

S o u t h w a l l

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5 0 0 r n r n B i t u m i n o u s c o n c r e t e

a) b ) 150 rn rn Pla in concre te

a ) P l a n a n d b ) c r o s s - s e c ti o n o f t h e r e v e r b e r a t i o n c h a m b e r .

- - R e v e r b e r a t i o n t im e :

a t 1 2 5 H z , T > 1 5 s ,

a t 500 Hz , T > 12 s , an d

a t 2000 Hz, T > 6 s .

- - S o u n d f ie ld d i s tr i b u ti o n :

i n th e l o w - f r e q u e n c y r a n g e A P = P m ~ x - P m i, < + 3 0 d B ,

i n t h e m e d i u m - a n d h i g h - f r e q u e n c y r a n g e A P = P ~ x - P m i, < + 1.5 riB ,

w h e r e max a n d P , , , r e p re s e n t r e sp e c ti ve ly t h e m a x i m u m a n d

m i n i m u m s o u n d p r e s s u r e l e v e l i n t h e m e a s u r i n g a r e a .

- - S o u n d d i f f u s i o n :

t h e p l a n n e d d i r e c t i o n a l d i f fu s i o n d > 0-95 w i t h o u t e x t r a s u s p e n d e d

d i ff u s e rs a n d s c a t t e r i n g e l e m e n t s in th e c h a m b e r ; a n d

- - B a c k g r o u n d n o i s e :

l es s t h a n 3 0 d B A .

T h e r e v e r b e r a t i o n c h a m b e r is b u i lt w i t h a n i r r e g u l a r s h a p e , w i t h e f fe c t iv e

c a p a c i t y o f 2 86 -6 m 3 a n d t o t a l s u r f a c e a r e a 4 1 4 m 2. B o t h t h e p l a n a n d c r o s s -

s e c ti o n o f t h e c h a m b e r a r e s h o w n in F i g. 1. T h e a c o u s t ic m e a s u r e m e n t s

c o n d u c t e d a f t e r th e c o m p l e t io n o f t h e r e v e r b e r a t i o n c h a m b e r h a v e i n d i c at e d

t h a t a l l t h e d e s i g n r e q u i r e m e n t s a r e m e t .

2 A C O U S T I C D E S I G N

2.1 V o l u m e

T o e s ta b l is h a d i ff u se s o u n d f i eld in t h e c h a m b e r , a d e q u a t e n o r m a l m o d e s

m u s t b e s t i m u l a t e d in t h e m e a s u r i n g f r e q u e n c y r a n g e , e s p e c ia l ly in t h e l o w -


3/9

cous t i c de sign o f a reverbera t ion cham ber 85

f r e q u e n c y ra n g e. T h e n u m b e r o f n o r m a l m o d e s w i t h in t h e f r e q u e n c y b a n d

A f n e a r t h e f r e q u e n c y f c a n b e o b t a i n e d f r o m e q n (1): 2

r 4 n f V r t f s L ]

a N = L ~ +~--~o2 ~-~-o_af 1 )

w h e r e V = v o l u m e o f t h e c h a m b e r ( m3 ); s = t o t a l s u rf a c e a r e a o f th e c h a m b e r

(m 2 ); L = t o t a l l e n g t h o f t h e e d g e s o f t h e c h a m b e r (m ) ; C o = s o u n d v e l o c i t y i n

a ir ; a n d A N = n u m b e r o f n o r m a l m o d e s .

A c c o r d i n g t o e q n (1 ), w h e n t h e f r e q u e n c y f i s h i g h t h e s e c o n d a n d t h i rd

t e r m s c a n b e i g n o r e d ; t h e n t h e e q u a t i o n m a y b e si m p l if ie d t o :

r c f z V

AN _ ~ C~ A f (2 )

I n g e n e r a l m e a s u r e m e n t s , t h e l / 3 o c t a v e b a n d is o f t e n u s e d, o f w h i c h t h e

r a t io b e t w e e n t h e f r e q u e n c y b a n d w i d t h A f a n d i ts c e n t r a l f r e q u e n c y fm

e q u a l s 0 2 3 . I n t h i s c a s e e q n (2 ) c a n b e w r i t t e n a s:

A N = 7.4(-ff--V~ (f---m~3

\ V o j t fo 3 )

w h e r e j m = c e n t r a l f r e q u e n c y o f I /3 o c t a v e b a n d ; Vo = r e f e re n c e v o l u m e

1 0 0 m 3 ; a n d f o = r e f e r e n c e f r e q u e n c y = 1 00 H z .

F r o m e q n ( 3) , t h e a p p r o x i m a t e n u m b e r o f n o r m a l m o d e s w i th i n a 1 /3

o c t a v e b a n d , o f w h i c h c e n t r a l f r e q u e n c y is fro , c a n b e o b t a i n e d .

T o e s t a b li s h a p e r f e c tl y di ff u s e s o u n d f i eld , a t l ea s t 1 5 - 2 0 n o r m a l m o d e s

s h o u l d b e e x ci te d w i t h i n t h e 1 /3 o c t a v e b a n d o f w h i c h t h e c e n t r a l f r e q u e n c y

is 1 0 0 H z . A c c o r d i n g t o e q n ( 3 ) , t h e e ff e c ti v e v o l u m e V is c a l c u l a t e d a s

2 0 0 - 2 7 0 m 3. T h e r e f o r e , t h e v o l u m e o f o u r c h a m b e r i s d e s i g n e d a s 2 68 -6 m 3.

2 2 Shape

T h o u g h h a v i n g l it tl e i n fl u en c e o n t h e n u m b e r o f n o r m a l m o d e s , t h e s h a p e o f

t h e c h a m b e r d o e s a ff ec t t h e d i s t r i b u t i o n o f n o r m a l f r eq u e n c ie s , p a r t i c u l a r l y

i n t h e l o w - f r e q u e n c y r a n g e . I S O h a v e r e c o m m e n d e d , 3 t h e r e fo r e , t h a t t h e

r a ti o b e t w e e n a n y t w o d i m e n s i o n s s h o u l d n o t b e a r o u n d n u m b e r . T h e

r e c o m m e n d e d ra t io s o f w i d t h / l e n g t h a n d h e i g h t / l e n g t h a r e s h o w n in

Tab le 1 .

I n o u r c h a m b e r , t h e w i d t h / l e n g t h a n d h e i g h t / l e n g t h r a t io s a r e r e sp e c t iv e l y

0-82 and 0 .66 .

T o p r e v e n t f l u t t e r e c h o e s p r o d u c e d b e t w e e n t w o p a r a l l e l w a l l s a n d t o

o b t a i n a u n i f o r m s o u n d d i s t r i b u t i o n i n t h e l o w - f r e q u e n c y r a ng e , t w o w a l ls o f

t h e r e v e r b e r a t i o n c h a m b e r a r e t i lt e d , w i t h t i l t in g a n g l e s 1 5 -- a n d 5

r e s p e c t i v e l y a n d t h e a c u t e a n g l e s c u t o f f .


4/9

86

Xiang Dua nqi, Wa ng Zheng, C hen Jinjing

T A B L E 1

R e c o m m e n d e d R a t i o s o f W i d t h / L e n g t h a n d H e ig h t/ '

L e n g t h

Width/length Height~length

0-83 0 65

0-79 0 63

0-68 0 42

0.70 0 59

2 3 Reverberat ion t ime

T h e a b s o r p t i o n a r e a o f e a c h s u rf a c e i n t h e r e v e r b e r a t i o n c h a m b e r m u s t b e

m a d e a s s m a l l as po s s ib l e s o t h a t t h e r e v e r b e r a t i o n t i m e c a n b e k e p t l o n g

e n o u g h t o m e a s u r e t h e a b s o r p t i o n p r o p e r ti e s o f m a t e ri a ls p a r t ic u l a rl y

m a t e r i a l s w i t h l o w a b s o r p t i o n c o e f fi c ie n t s. It is s p e c i fi e d b y I S O 3 t h a t i n a n

e m p t y c h a m b e r w i t h a v o l u m e o f 2 00 m 3 t h e t o ta l a b s o r p t i o n a re a m u s t b e

le ss t h a n t h e v a l u e s l is te d in t h e f i rs t r o w o f T a b l e 2 w h e n t h e m e a s u r e m e n t is

c o n d u c t e d i n 1 /3 o c t a v e b a n d s . I f t h e v o l u m e o f a r e v e r b e r a t i o n c h a m b e r i s I7

t h e a l lo w e d m a x i m u m a b s o r p t i o n a re a i n th e c h a m b e r s h o u l d b e th e a b o v e-

s t a t e d v a lu e s m u l t i p l i e d b y

( V / 2 0 0 ) 2/3 .

T o r e d u c e t h e a b s o r p t i o n a re a t h e

w a l ls a r e o v e r l a i d w i t h c e r a m i c t il es w i t h p o i n t i n g o f w h i t e c e m e n t a n d t h e

f l o o r a n d s u r f ac e o f s p h e r i c a l di ff u se r s a r e p a v e d w i t h w a x e d t e rr a z zo . T h e

r e v e r b e r a t i o n c h a m b e r a n d t h e s p h e ri c a l d i ff u se r s a r e m a d e u p o f r e i n f o r c e d

c o n c r e t e i n o r d e r t o p r e v e n t lo w - f r e q u e n c y r e s o n a n t a b s o r p t i o n .

2 4 Di f f u s ion

I t is v e r y i m p o r t a n t f o r a r e v e r b e r a t i o n c h a m b e r t o h a v e a s u ff i c ie n t ly d i ff u s e

s o u n d f ie ld . T h e v o l u m e o f 2 68 .6 m 3 a n d l o w a b s o r p t i o n a r e a s w e r e d e s i g n e d

t o g i v e g o o d d i f f u s i o n b u t d i f f u s i o n w o u l d u n d o u b t e d l y b e e f f e c t e d

p a r t i c u l a r l y w h e n m e a s u r i n g t h e a b s o r p t i o n c o e f fi c ie n t o f m a t e r i a l s w h e n

T A B L E

T h e A l l o w a b l e M a x i m u m A b s o r p t i o n A r e a ( S ab i ne )

Volume FrequenO ( Hz}

{m 3

125 250 500 1 000 2 000 4 000

200 6-5 6-5 6-5 7-0 9-5 13'0

268-6 7 9 7.9 7-9 8-5 1 '5 15'8


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coustic design of a reverberation chamber 87

r : 1 2 ~ r = 6 5

. . . . ,

1 1

I i , _ ~

r: 9 ~0

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i

a)

Sou~h wa l l

8610

o

4 6 6 2 i

8610

i

i

d)

Fig. 2. Dim ensions,shape, and arrange m ents of diffusers. a) Sizes and shape of diffusers. b)

Arrangem ent on southern wall. c) Arrangem ent on the ceiling. d) Arrangem ent on eastern

wall.

t h e fl o o r is c o v e r e d w i t h l O m 2 o f a b s o r b e n t m a t e r ia l . T o o b t a i n a p e rf e c t

d i f f u s e s o u n d f i e l d , t h e f o l l o w i n g m e t h o d s a r e u s u a l l y a d o p t e d .

- - S u s p e n d e d s c a t t e r i n g e l e m e n t s o r d if f u se r s i n t h e c h a m b e r , b u t t h is w ill

g r e a t ly r e d u c e t h e r e v e r b e r a t i o n t im e .

- - I n s t a l l i n g a r o t a t i n g p a d d l e in th e c e n t e r o f t h e c h a m b e r , b u t t h is w ill

c o n s i d e r a b l y r e d u c e t h e m e a s u r i n g s p ac e . T h e r e w ill a l so b e n o is e f r o m

t h e m o t o r d r i v i n g t h e p a d d l e w h i c h i s d i ff ic u l t t o e l im i n a t e .

T o r e m e d y t h e d e f e c t s m e n t i o n e d a b o v e , f o u r d i f fe r e n tl y s iz e d s p h e r ic a l

d i ff u se r s m a d e o f r e i n f o r c e d c o n c r e t e a r e u s e d i n th e c h a m b e r , o f w h i c h t h e

r a d i i o f c u r v a t u r e a r e 1 .2 5 m , 0 - 9 5 m , 0 -6 5 m a n d 0 -5 m , r e s p e c t i v e l y . T h e

d i ff u s e rs a r e f i x ed o n t w o n e i g h b o r i n g w a l ls a n d t h e c e il in g i n a n i r r e g u l a r

a r r a n g e m e n t , s o t h a t n o p a i r o f s m o o t h s u r f a c e s w ill fa c e e a c h o t h e r i n th e

c h a m b e r . T h e d i m e n s i o n s , s ha p e , a n d a r r a n g e m e n t o f t h e di ff u se rs a r e

s h o w n i n F ig , 2. F i g u r e 3 is a p h o t o g r a p h o f t h e i n si d e o f t h e r e v e r b e r a t i o n

c h a m b e r .

2 5 Backgrou nd noise

T h e r e v e r b e r a t i o n c h a m b e r is s i tu a t e d i n a n i n d u s t r ia l a r e a n e a r t h e a i r p o rt ,

w h e r e t h e n o i s e is u p t o 8 5 d B A d u r i n g t a k e - o f f a n d l a n d i n g o f a ir p la n e s . T o


6/9


7/9

A c o u s t i c d e s ig n o f a r e v e rb e r a t io n c h a m b e r 89

~7- - -t~- - -p'4----9 - - ~ 1 //..

I l

~-- -- --- ---4

~9-- -- &-- --~ - -b----~ 3

everberation time and

directional diffusion

;

o S o u n d f i e l d d i s t r i b u t . i o n

Fig. 4. Locations of measurements.

deviat ion. The ab sorpt ion areas calculated on the basis of reverberat ion t ime

are less than the allowable maximum values l isted in Table 2.

3.2 Sound field

distri ution

The soun d field distri bution was meas ure d fro m 125 Hz to 4000 Hz at 25

positions and two levels. The sound source was octave band white noise and

the signals were received in the 1/3 octave band. The difference between the

ma xi mum and mi nim um s ound pressure levels measured at six locat ions and

the standard deviations are l isted in Table 3. The results obtained have

indicated that the sound field distribution is uniform and the design

requirements have been satisfied.

TABLE 3

The Results of Measurement

C o n t e n t

O c t a v e c e n t ra l f r e q u e n c y

(H:)

125 25 5 1 2 4

Reverberation time a

7 6 0 21-07 13 67 12 3 9 9 7 8 5-I

6 I'1 0-42 0 26 0 23 0 20 0 16

Sound field distribution

AP 5'5 2-5 2'5 2 5 1.5 1 5

6 1 46 0-62 0-56 0 58 0-35 0-35

Absorption area b 2 1 3'2 3-5 4.4 5.5 8.5

Background noise 34.5 23 0 20.7 14-0 12.7 12 2

25 4 dBA

Only octave data are listed.

b Calculated on the basis of reverberation time.


8/9

9 0

Xiang Duanqi Wa ng Zheng Chen Jinjing

P 5

t 1 2 5 H z ~ 2 5 0 H z 5 0 0 H z l O 0 0 H z 2 0 0 0 H z 4 0 0 0 H z

I.q ~ d . lAa l L= t= J ~ ~ I . tJ_~ t . . .

f '% H ,l. L . ~ V V IM 'IL , V 'V ~ lm ., t ~ V ' ~ , ~

' v .

P ; p ~ , - s p , ,, , ,d 1 0 , - . m ls If Iv~ ~A., ' ~ 1 ~ 1 , . I.. ~V~A., ~ , ~ ' ~ \

re ,

0 l O d B

F i g 5 R e v e r b e r a t i o n d e c a y c u r v e s

3 3 S o u n d d i f fu s i o n

I t h a s b e e n i n d i c a t e d t h a t a b e t t e r d i f f u s io n o f t h e s o u n d f ie ld is o b t a i n e d

o w i n g t o t h e n o n - p a r a l l e l w a l ls w i t h r e i n f o r c e d c o n c r e t e s p h e r ic a l d if fu s er s,

w h i c h c a n b e p r o v i d e d a s f o l l o w s .

( a) T h e r e v e r b e r a t i o n d e c a y c u r v e s o b t a i n e d a t 2 7 p o i n t s (n i n e l o c a t i o n s

a n d t h r e e le ve ls ) a n d 17 f r e q u e n c i e s a r e s m o o t h a n d s t r a i g h t a n d t h e

s t a n d a r d d e v i a t i o n s a r e s m a l l ( se e T a b l e 3). S o m e d e c a y c u r v e s a r e s h o w n i n

Fig. 5 .

(b ) T h e s o u n d f ie ld d i s t r i b u t i o n i n t h e c h a m b e r is q u i t e u n i f o r m ( se e T a b l e

3).

(c) T h e m e a s u r e m e n t o f d i r e c t i o n a l d i f f u s io n p r o p o s e d b y T h i e le ~ is q u i t e

c o m p l e x a n d d i ff i cu l t t o c o n d u c t , s o a p l a n a r d i r e c t i o n a l d i f fu s i o n is

m e a s u r e d in t h e c h a m b e r b y u s in g a s ta t i o n a r y s o u n d s o u r c e e m i t ti n g w a r b le

t o n e s o f 2 0 00 H z a n d a h i g h d i re c t i o n a l r e c e iv e r c o m p o s e d o f a se c t o r s o u n d

l en s w i th a c o n d e n s e r m i c r o p h o n e a t i ts f o c u s. A s t h e r e c e i v e r r o t a t e s i n a

p l a n e f r o m 0 to 3 60 , th e v o l t a g e o u t p u t f r o m t h e m i c r o p h o n e is d r a w n

c o n t i n u o u s l y o n p o l a r c o o r d i n a t e r e c o r d p a p e r . T h e p l a n a r d i r e c t i o n a l

d i f fu s i o n d i s

m

d = 1 - - (4)

gg/o

w h e r e d = p l a n a r d i r e c t i o n a l d i ff u s io n ; m = d i f fu s i o n c o e f f ic i e n t i n t h e

m e a s u r e d c h a m b e r , a n d m o = d i ff u s io n co e f fi c ie n t i n th e a n e c h o i c c h a m b e r .

T h e d i f f u s i o n c o e f f i c i e n t is:

A M

m -- (5)

M


9/9

c o u s t i c d e si g n o f a r e ve r b e r a ti o n c h a m b e r 9

w h e r e M i s t h e m e a n s o u n d i n t e n s i t y f r o m a l l d i r e c t i o n s :

M = f f ~ Adq3

= I - - F I ~ : ~ x / -A ) Z d ~ 0 1 6 )

2 n n L 2

o

a n d A M is th e m e a n d e v i a t i o n o f s o u n d i n te n s it y :

i = A - M ld~o

= L F f < 7

o

2x 7: L 2 Jo l i v A V

M

w h e r e 4 is t h e s o u n d i n t e n s i t y .

T h e c o e ff ic ie n t m o c a n b e o b t a i n e d b y m e a n s o f t h e s a m e m e t h o d a s m .

T h e m e a n v a l ue o f p l a n a r d i r e c t i o n a l d i ff u s io n m e a s u r e d a t n i n e l o c a ti o n s

( th e s a m e o n e s a s t h o s e u s e d f o r m e a s u r i n g t h e r e v e r b e r a t i o n t im e ; s ee F i g. 4)

i s 0 9 6 , t h u s m e e t i n g t h e d e s i g n r e q u i r e m e n t s .

3 . 4 B a c k g r o u n d n o i s e l e v e l

T h e b a c k g r o u n d n o i s e l e v e l i n s i d e t h e c h a m b e r w a s m e a s u r e d w h e n t h e

n e a r b y w o r k s h o p w a s in o p e r a ti o n . T h e n o is e s p e c t r u m a n d d B A a r e s h o w n

i n T a b l e 3. I t is c l e a r l y s h o w n t h a t t h e m e a s u r e d n o i s e l e v el s a r e l e ss t h a n t h e

d e s i g n t a r g e t .

4 C O N C L U S I O N

T h e m e a s u r e m e n t s s h o w t h a t a l l t h e a c o u s t ic c r i t e ri a f o r th e r e v e r b e r a t i o n

c h a m b e r h a v e b e e n r e a c h e d , s o m e e v e n b e e n s u r p a s s e d . T h e r e v e r b e r a t i o n

c h a m b e r h a s b e e n s h o w n t o h a v e e x c e ll e n t a c o u s t i c p r o p e r t i e s d u r in g t h e

p a s t 1 8 m o n t h s . T h i s p r o j e c t h a s p r o v e d t h a t i t i s p o s s i b l e t o e s t a b l i s h

s u ff ic ie n t d i ff u s io n in a r e v e r b e r a t i o n c h a m b e r w i t h o u t e x t r a s u s p e n d e d

d i ff u s e rs o r s c a t t e r i n g e l e m e n t s . T h e u s e o f ir r e g u l a r s h a p e a n d t il te d w a ll s

w i t h f i x e d r e i n f o r c e d - c o n c r e t e s p h e r i c a l d i ff u s e rs is o n e o f th e b e t t e r

m e t h o d s o f o b t a i n i n g a d if fu s e s o u n d f ie ld in a r e v e r b e r a t i o n c h a m b e r .

R E F E R E N C E S

1. X i a n g D u a n q i, W a n g Z h e n g & C h e n J in ji ng ,

AppL Acous t . ,

29 (1990) 139.

2. Morse, P. M.,

Vibrat ion and Soun d,

McGraw-Hi l l , 1948 .

3 . ISO 354 19 85 E.

4. Thiele, R., Acous t ics , 3 (1953 ) 291.

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