Acoustic Design of a Reverberation Chamber
Transcript of 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
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84 Xiang Duanqi Wang Zheng. Chen Jinling
S o u t h w a l l
-1-~ .- +
r L l ' - - , ,
~'=:~, ~ l l
~ I
-93oo
i
v l I 1
Fi g . I .
: o -oo
SO mm Reinforced
c o n c r e t e f e l t
I O O m m M i n e r a l w o o l
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 -
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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 .
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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
r : 5
0
+
,6 oo + e r e t _ _ _ ~
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
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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.
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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
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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.