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Optical Representation of Sound Fields with Phase and Amplitude
Recording
Schroeder, H. J.
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PREFACE I t i s f r e q u e n t l y n e c e s s a r y i n a c o u s t i c a l measure- ments t o be a b l e t o p l o t t h e p r e s s u r e sound f i e l d i n terms of I s o b a r s ( c u r v e s of e q u a l p r e s s u r e ) . Normally t h i s i s done by t e d l o u s l y r e c o r d i n g p r e s s u r e l e v e l s i n t h e space i n q u e s t i o n , s e a r c h i n g f o r p o i n t s of e q u a l p r e s s u r e , t h e n j o i n i n g them w i t h a c u r v e . The a u t h o r of t h i s paper d e s c r i b e s a method I n which t h e c o n t o u r s i n a plane a r e recorded a u t o m a t i c a l l y by u s i n g t h e e l e c t r i c a l o u t p u t of a mlcrophone t o modulate a l i g h t s o u r c e , t h e n photographing i t . The a m p l i t u d e s I n a given p l a n e a r e picked o f f i n
5
db c o n t o u r s . T h i s i s a u s e f u l method f o r p l o t t i n g c o n t o u r s of s t a n d i n g waves, e . g , i n a r e s o n a n t e n c l o s u r e . The a u t h o r goes f u r t h e r and shows t h a t i t i s a l s o p o s s i b l e t o r e - p r e s e n t p r o g r e s s i v e waves. To do t h i s a phase d e t e c t o ri s included i n t h e r e c e i v i n g system and t h e phase of t h e r e c e i v e d s l g n a l i s compared t o t h a t of t h e s o u r c e . T h i s undoubtedly f i n d s a p p l i c a t i o n s i n measurements made i n f r e e space o r a n e c h o i c chambers, e . g . i n t h e p a t t e r n produced by s c a t t e r i n g o b j e c t s o r t h e d i r e c t i v i t y p a t t e r n s of sound s o u r c e s . F i n a l l y , t h e a u t h o r , a f t e r showing how t h e t e c h n i q u e works f o r simple s o u r c e s ,
c o n s i d e r s more e x o t i c examples such a s b e l l s and v i o l i n s . The D i v i s i o n of B u i l d i n g Research wishee t o record i t s g r a t i t u d e t o M r . D . A . S i n c l a i r , Head, T r a n s l a t i o n s S e c t i o n , N a t i o n a l Research Council, f o r t r a n s l a t i n g t h i s paper and t o D r . R . J . Donato of t h i s D i v i s i o n who checked t h e t r a n s l a t i o n .
Ottawa R . F . Legget
NATIONAL RESEARCH COUNCIL OF CANADA Technlcal Translation 1258
Title: The optical representation of sound fields with phase and
amplitude recordlng
( ~ p t i s c h e Schallfelddarstellung mit Phasen- und Amplitudenaufze~chnung)
Author : H. -J , Schroeder
Reference: Acustica,
13
(2): 92-10:3, 1963TIIE OPTICAL REPRESENTATION OF' S O U N D FIELDS \;I IT11 Pi-IASE A N D AMI'LI:'J.'ODE RECORDING
A b s t r a c t
The c o n 3 t r u c t i o n and mode o r operation of a n a p p a r a t u s a r e d e s c r i b e d , which p e r m l t s t h e o p t i c a l repr'esentatl.on of s t a t i o n a r y sound f i e l d s i n a i r . Prom t h e method proposed by Kock and Harvey f o r t h e o p t i c a l r e p r e s e n t a t i o n of p r o g r e s s i v e waves a new method h a s been developed, which p e r m i t s a l s o t h e r e c o r d i n g of i s o b a r s of t h e sound p r e s s u r e . The sound p r e s s u r e p a t t e r n of a sound f i e l d
i s now r e p r e s e n t e d by s i x i s o b a r s w i t h a l e v e l difference of
5
db. T h i s method i s a p p l i e d t o t h e f i e l d s of v a r i o u s sound s o u r c e s , a s p h e r i c a l r a d i a t o r , a group of two s i n g l e r a d i a t o r s , a b e l l , a c y l i n d r i c a l t u b e and a v l o l i n .1. I n t r o d u c t i o n
P r a c t i c a l l y s p e a k i n g t h e r e i s o n l y one rnethod of r e p r e s e n t i n g sound f i e l d s i n a i r o p t i c a l l y , namely by scanning w i t h a probe ml-crophone. The a c o u s t i . c a 1 p r o c e s s i s t h e r e b y converted i n t o an o p t i c a l one which i s imaged a t t h e probe a p e r t u r e . The image I s produced a s a r e s u l t of t h e microphone and lamps s c a n n i n g a p l a n e of t h e sound f i e l d i n a darkened s p a c e . T h i s p r o c e s s i s photographed ( ~ i g 1 ) .
I n 1950 Kock and Iiarveyil) r e p o r t e d t h e v i s u a l i z a t i o n of sound waves and e l e c t r o m a g n e t i c 1,iaves i n t h e c e n t i m e t r e r e g i o n . C h i e f l y emphasized was t h e r e p r e s e n t a t i o n of p r o g r e s s i v e waves. T h i s kind of r e p r e s e n t a t i o n
i s o b t a i n e d when a phase-locked comparison v o l t a g e i s superimposed on t h e v o l t a g e g e n e r a t e d a t t h e microphone, and t h e t o t a l v o l t a g e i s used t o
c o n t r o l t h e lamp. The r e s u l t i n g image is more o r l e s s a n i n s t a n t a n e o u s p i c t u r e of t h e sound f i e l d
.
The amplitude distribution i n t h e f i e l d was r e p r e s e n t e d by t h e f a c t t h a t t h e b r i g h t n e s s of t h e lamp was c o n t r o l l e d by t h e sound p r e s s u r e . Thus a p i c t u r e i s o b t a i n e d i n which r e g i o n s of h i g h sound p r e s s u r e a p p e a r b r i g h t . However, t h i s method i s n o t v e r y s u i t a b l e f o r quantitative e v a l u a t i o n , which i s extremely complicated a t b e s t ( e v a l u a t i o n by t h e g r e y s c a l e ) .
I n r e c e n t y e a r s s e v e r a l a u t h o r s (2-5) have d e a l t w i t h Kock and Harvey1 s method w i t h o u t f i n d i n g a s a t i s f a c t o r y s o l u t i o n t o t h e amplitude r e r o r d i n g problem. The p r e s e n t paper o f f e r s a new p o s s i b i l i t y of a c c u r a t e r e p r e s e n t a - t i o n of t h e sound f i e l d with r e s p e c t t o phase and a m p l i t u d e ( ' ) . The
u n c e r t a i n t y of r e c o r d i n g i s l e s s t h a n 1 cm, t h e l e v e l u n c e r t a i n t y i n t h e drawing of t h e :Lsobars, l e s s t h a n 0 . 3 d b . F i e l d segments of a p p r o x i m a t e l y
2
2 . The ConutrS~rc:t \.on of t h e l4easurl.ny A p p a r a t u s 2 . 1 . klechan l c a l p a r t
The m e c h a n i c a l p a r t of t h e a p p a r a t u s c o m p r l s e s t h e d e v i c e f o r s c a n n i n g t h e sound f l e l d . T t s p u r p o s e 1s t o g u l d e t h e lamp and t h e microphone t h r o u g h t h e sound f i e l d a l o n g t h e d e s i r e d p a t h . S p l r a l - s h a p e d s c a n n t n g p a t h s a r e employed. F o r p u r p o s e s of p h o t o g r a p h ! ~ recording t h e d i s t a n c e between two c o n s e c u t l v e r a s t e r l l n e s must be c o n s t a q t and l e s s t h a n t h e l i g h t e x l t a p e r t u r e . T h i s p r e v e n t s any unexposed s t r i p s from appearing o n t h e f i l m between l l n e s . The d l s t a n c e between c o n s e c u t i v e s p i r a l p a t h s m ~ s t be small enough s o t h a t no i n t e r f e r l n g l l n e s a p p e a r on t h e sound f i e l d p i c t u r e , The d i s t a n c e bet-reen l l n e s must a l s o be a d a p t e d t o t h e " a c o u s t i c r e s o l v i n g power" d e p e n d i n g on t h e dirnenslons of t h e microphone p r o b e .
The a p p a r a t u s i s c o n s t r u c t e d a s f o l l o w s ( ~ i g . 2 ) .
A p i p e 30 mm i n d i a m e t e r and a b o u t 3 m l o n g r o t a t e s a b o u t a h o r i z o n t a l a x i s . On t h i s p i p e i s mounted a s l i d e 7,ihich c a n move p a r a l l e l t o t h e a x i s of t h e p i p e . b u t c a n n o t r o t a t e a b o u t t h e p i p e a x i s . On one end o f t h e s l i d e t h e microphone 1s mounted, s o t h a t ;vhen t h e s l i d e i s s t a t i o n a r y it d e s c r i b e s a c i r c l e i n a v e r t i c a l p l a n e . A r a c k i s mounted on t h e s l i d e which e n g a g e s w i t h a p i n i o n . The l a t t e r i s c o n t r o l l e d s o t h a t t h e s l i d e moves
2 . 7
mrna l o n g t h e p i p e e v e r y r e v o l u t i o n . As a consequence, t h e microphone f o l l o w s a s p i r a l p a t h .
The d r i v i n g mechanism i s d e s i g n e d t o keep t h e s c a n n i n g speed c o n s t a n t . The e x p o s u r e of t h e f i l m t h u s d e p e n d s e x c l u s i v e l y on t h e b r i g h t n e s s o f t h e
lamp.
or
c o n s t a n t i n t e n s i t y o f t h e l i g h t , a change i n t h e s c a n n i n g speed would a f f e c t t h e e x p o s u r e t i m e ) . The u p p e r speed l i m i t i s g i v e n by t h e development of wind n o i s e s and i n t e r f e r e n c e s due t o t h e Doppler e f f e c t .For a u t o m a t i c c o n t r o l of t h e rpm a c o n t i n u o u s l y v a r i a b l e speed t r a n s - m i s s i o n i s employed The microphone speed i s 1 . 3 m p e r second and i s k e p t
c o n s t a n t t o approximately f10$.
2 . 2 . A c o u s t i c - e l e c t r i c p a r t
The microphone must meet t h e f o l l o w i n g r e q u i r e m e n t s :
1. I t s d i r e c t i o n a l c h a r a c t e r i s t i c m u s t , a s f a r a s p o s s i b l e . b e s p h e r i c a l .
2 . Sound f i e l d d i s t o r t i o n s d u e t o t h e microphone must b e k e p t a s s m a l l a s p o s s i b l e .
3 . The microphone must show s u f f i c i e n t s e n s i t i v i t y .
P u t t i n g t h e u p p e r l i m i t i n g f r e q u e n c y a t
15
k c , we g e t a n e s t i m a t e dand 0 1 1 account of h15 kc = 2 . 2 cm:
d < 1.1 cm.
More s u i t a b l e t h a n t h e u s e of such a microphone i s t h e u s e of a probe
microphone. I n t h i s c a s e o n l y t h e probe needs t o be dimensioned a c c o r d i n g t o t h e requirement,^. t h e a c o u s t i c a l s t a n d p o i n t , t h e l e n g t h of t h e probe shouttd be a s g r e a t a s p o s s i b l e , i n o r d e r t o keep d i s t u r b a n c e s of t h e
sourtd f i e l d due t o nearby p a r t s of t h e r o t a r y framework s m a l l . On t h e
o t h e r hand, t h e d i a m e t e r of a probe a u s t be k e p t a s s m a l l a s p o s s i b l e i n o r d e r t o avoid sound f i e l d d i s t o r t i o n s due t o t h e probe i t s e l f and t o g e t a s p h e r i - c a l c h a r a c t e r i s t i c f o r h i g h f r e q u e n c i e s . N e i t h e r requirement c a n be f u l l y r e a l i z e d because t h e p i p e damping would be t o o g r e a t .
The dimensions of t h e probe, a c c o r d i n g l y , should be s o chosen a s j u s t t o e n s u r e r e a l i z a t i o n of p o i n t s 1 and 2 f o r t h e l i m i t i n g f r e q u e n c y .
The probe was designed t o have a l e n g t h of about 750 m m , an i n s i d e
d i a m e t e r of 8 rnm and an o u t s l d e d i a t n e t e ~ of 10 mm. For f = 1 5 kc ( A = 2.2 cm) a p i p e damping of approximately 6 db i s o b t a i n e d .
The d i r e c t i o n a l c h a r a c t e r i s t i c of t h e probe can be determined a p p r o x i - m a t e l y by o b t a i n i n g t h e d i r e c t i o n a l f a c t o r of a c i r c u l a r p i s t o n membrane, t h e d i a m e t e r d of which i s e q u a l t o t h e i n s i d e d i a m e t e r of t h e p i p e : 'i. R ' = 2 J,
(-A-
s i n y - * d) ,
J,(x)
R = g - 7td-
X f o r x =-
h s i n y . idhere J, ( x ) i s t h e B e s s e l f u n c t i o n of f f r s t o r d e r , y i s t h e a n g l e of d i r e c - t i o n , forming t h e c o r r e s p o n d i n 3 s t r a i g h t l i n e p r o j e c t i o n w i t h t h e z a x i s . The system of c o o r d i n a t e s i s s o chosen t h a t t h e z a x i s c o i n c i d e s w i t h t h e p i p e a x i s , and t h e opening of t h e p i p e l i e s i n t h e x, y p l a n e . The p r i n c i p a l a x i s i s t h e n s i t u a t e d a t y = 0 ° , 1 . e . i n t h e d i r e c t i o n of t h e z a x i s .I n t h e t e s t s e t - u p , t h e t i p of t h e probe 1 3 s i t u a t e d i n t h e x, y p l a n e . The t e s t o b j e c t can be s i t u a t e d e i t h e r i n t h e x, y p l a n e , o r i n f r o n t of i t . I n t h e former c a s e t h e f i e l d i s photographed o n l y i n t h e one d i r e c t i o n of p r o p a g a t i o n vihich i s of i n t e r e s t ( f o r * n s t z n c e l o u d - s p e a k e r r e c o r d s ) . I n
*
T r a n s l a t o r ' s n o t e : An u n d e r l i n e d symbol s i g n i f i e s g o t h i c t y p e s c r i p t i n t h e o r i g i n a l .t h i s c a s e y i s always 9 0 ° , and t h e d i r e c t i o n a l c h a r a c t e r i s t i c , on a c c o u n t of t h e r o t a t i o n a l symmetry of t h e p r o b c , p l a y s no p a r t . However, if t h e t e s t o b j e c t i s s i t u a t e d i n f r o n t of t h e x, y p l a n e , a s i a o f t e n t h e c a s e , t h e n y
may be anywhere between 0 and 9 0 " .
For y 5 go0, s i n y = 1 and f = 1 5 k c , h15 kc = 2 . 2 cm f o r d = 0.8 cm g i v e s a r a t i o of
Thus
S i n c e f o r y = O 0
-
R = I , t h e d e p a r t u r e from t h e s p h e r i c a l c h a r a c t e r i s t i cT h i s i s t h e l e a s t f a v o u r a b l e c a s e p o s s i b l e .
To sum up, we may s a y t h a t up t o f = 1 0 kc t h e requirement o f a
s p h e r i c a l c h a r a c t e r i s t i c i s p r a c t i c a l l y s a t i s f i e d . For f > 1 0 kc a n e r r o r a r i s e s which can be reduced e i t h e r by r e d u c i n g t h e d i a m e t e r of t h e probe, o r by a v o i d i n g a v e r y l a r g e a n g l e .
2 . 3 . E l e c t r o n i c p a r t
The s i g n a l from t h e microphone i s f e d t o a p r e a m p l i f i e r ( ~ i g .
3 ) .
D e s p i t e c a r e f u l atmospheric and v i b r a t i o n i n s u l a t i o n o f t h e d r i v e mechanisms, i n t e r f e r e n c e s g e t t o t h e microphone and t h e s e m u s t f i r s t be removed. The h i g h p a s s f i l t e r , p r i m a r i l y , s e r v e s t h i s purpose, because t h e i n t e r f e r e n c e l e v e l components from t h e motor c o n t a i n p r e d o m i n a t l y low f r e q u e n c i e s .
A d d i t i o n a l f i l t r a t i o n i s c a r r i e d o u t w i t h t h e a i d of a t h i r d o r d e r f i l t e r . \!hat i s t h e form of t h e u s e f u l v o l t a g e when t h e s o u r c e e m i t s a
s i n u s o i d a l sound? On p a s s i n g through t h e sound f i e l d a s i g n a l i s r e c e i v e d which i s a m p l i t u d e , f r e q u e n c y and phase modulated. The a m p l i t u d e modulation a r i s e s from t h e f a c t t h a t t h e r e c e i v e r i s moving t h r o u g h r e g i o n s of
d i f f e r e n t sound p r e s s u r e . The modulation f r e q u e n c y i s c o m p a r a t i v e l y low.
and f r e q u e n c y rnoduL:ltlon;; :II.C clue t,r, Lhc Lilct, L h a t t h e d i s t a n c e between t h e rnicroyholle a n d t h c s t a t . l o ~ ~ a r y s u u t ~ d :;our3cc is: c o n l , i n u a l l y c h a n g l n g i n t h e c o u r s e of t h e s c a n u l n g proccs; ( ~ ) o , p ~ l e r . e f f e c t )
.
T h e a m p l i t u d e a n d phase tnodulationa arlc used t o c o n t r o l t h e l i g h t s o u r c e . The f r e q u e n c y ~ n o d u l a t l o t l it; n o t e v a l u a t e d a s s u c h . A t t h e maximum i t c a n
o n l y be 0.45 and would be a d l u t u r b l n g S a c t o r o n l y i f v e r y narrow band f i l t e r s were employed.
2 . 3 . 1 . Phase c h a n n e l
The p h a s e modulated s i g n a l i s used t o r e p r e s e n t t h e p r o g r e s s i v e wave
(1)
i n t h e sound f i e l d , :nucl-I a s i n t h e manner s u g g e s t e d by Kock and Harvey
.
A t d i s t a n c e s r = A, 2 h , 3 h ,
.
. .
s i m i l a r phase c o n d i t i o n s p r e v a i l . dhen we c o n s i d e r t h e phase a n g l e between t h e g e n e r a t o r v o l t a g e which f e e d s t h e sound s o u r c e and which may s e r v e a s a cornparlson v o l t a g e , and t h e rnicrophone v o l t a g e , t h e n t h e phase r o t a t e s 27r a s t h e microphone rnoves a d i s t a n c e A away from o r towards t h e s o u r c e . T h i s f a c t i s used t o r e p r e s e n t t h e p r o g ~ ~ e s s i v e wave by superimposing t h e ~ n i c r o p h o n e v o l t a g e on a phase-locked comparisonv o l t a g e . The t o t a l v o l t a g e 1s used t o modulate t h e lamp c u r r e n t . I n o r d e r t o o b t a i n a d e g r e e o f ~ o d u l a t i o n which i s i n d e p e n d e n t of t h e microphone d i s t a n c e , t h e v a l u e of t h e rnicrophone v o l t a g e must be k e p t c o n s t a n t w i t h t h e a i d o f a l i m i t e r . i n g e n e r a l , t h e g e n e r a t o r v o l t a g e can b e used f o r comparison p u r p o s e s . However, i t i s e q u a l l y p o s s i b l e t o u s e t h e o u t p u t v o l t a g e of a
second n i c r o p h o n e i n a f i x e d p o s i t i o n .
The manner of o p e r a t i o n o f t h e phase c h a n n e l i s i n d i c a t e d i n F i g . 4.
The o s c i l l o g r a m shows t h e c o n v e r s i o n of t h e microphone v o l t a g e ( a t t h e t o p o f t h e p i c t u r e ) i n t o t h e lamp c u r r e n t ( b e l o w ) . I n s c a n n i n g t h e sound f i e l d a segment was chosen i n which t h e microphone w a s moving towards a p o i n t sound s o u r c e and t h e n rnoving away from i t a g a i n . The f r e q u e n c y was 4 k c . It w i l l be noted t h a t t h e m o d u l a t i o n of t h e lamp c u r r e n t 1 3 l a r g e l y i n d e p e n d e n t o f
t h e microphone v o l t a g e . 2 - 3 . 2 . Amplitude c h a n n e l
I n o r d e r t o extend t h e e a r l i e r t y p e o f r e p r e s e n t a t i o n of t h e p r o g r e s s i v e wave, a n a p p a r a t u s was developed which makes p o s s i b l e t h e v i s u a l i z a t i o n of i s o b a r s ( l i n e s of e q u a l sound p r e s s u r e ) , s o t h a t b e s i d e s t h e p h a s e r e l a t i o n , t h e a m p l i t u d e d i s t r i b u t i o n can a l s o be made v i z i b l e . For t h i s p u r p o s e t h e a m p l i f i e d and f i l t e r e d microptione v o l t a g e i s r e c t i f i e d and f e d t o a v o l t a g e d i v i d e r ( F I E . 3 ) . The l a t t e r h a s 5 t a p s t a g e s , d e l i v e r i n g i n c r e m e n t a l v o l t a g e s C, t o TJ6 i n 5 - d b i n t e r v a l s . Each o f t h e s e v o l t a g e s c o n t r o l s a
v o l t a g e c i i s c r i t n i n a t o r ( m i c h : n i t t - T r i g g e r ) . If t h e v o l t a g e g o e s e i t h e r above o r belol;~ t h e l a t t e r s t h r e s h o l d v o l t a g e , a p o s i t i v e o ~ n e g a t i v e i m p u l s e , a s
t h e c a s e may b e , l o o b t a l n c d 3:; a11 o u t ; p ~ r t v o l t ; a ~ ~ e . ?'he 011t;put:; c f t h e s i x d i s c r l n l l n n t o r s a r e c o n n e c t e d 1 t 1 p a r a l l e l . l'h3.:; ay)piiral;un o p e r a t e : ; a s f o l l o w s :
A s t h e mlcrophotlt? v o l t a g e i n c r e a s e s , t h e lar[,rest; oi' t h e kapped v o l t a g e s
(u,
) r e a c h e s t h e I = C S ~ O I ~ Z C v a l u e of t h e corr.~::;~mndlnl: tij..;crlmlnat;or 1 , whicht h e n d e l i v e r s a n -L~npulse. \,!hen t h e sound l e v e l a t tiic p r o b e t i p h a s r i s e n by 5 d b , t h e second l a r g e s t v o l t a g e IJ, w i l l have J u s t r e a c h e d t h e v a l u e n e c e s - s a r y i n o r d e r ' t o p r o d u c e a r e s p o n s e o f d i s c r i m i n a t o r 2 . The i m p u l s e 2 a p p e a r s a t i t s o u t p u t . A s t h e sound l e v e l c o n t i n u e s t o r i s e v o l t a g e s U, t o C, I n t u r n r e a c h t h e t r i g g e r v o l t a g e of t h e i r d i s c r i r n ~ l n a t o r s , s o t h a t , i n e a c h c a s e a n irnpulse i s e m i t t e d a t i n t e r v a l s of
5
d b . The same t h i n g o c c u r s a s tbie l e v e l d r o p s : t h e I n d i v i d u a l v o l t a g e s c o n t r o l t h e i r d i : ; c r i m i n a t o r s i n t h e r e v e r s e o u t p u t s t a t e , t h u s g e n e r a t i n g irnpul.ses f o r t h e o p p o s i t e d i r e c t i o n .The i m p u l s e s a r e t h e n used t o c o n t r o l t h e lamp. I n t h i s manner p u l s e s of l i g h t a r e produced a s t h e sound l e v e l g o e s above o r belovr c e r t a i n d e f l n e d l e v e l s . Curves of e q u a l sound p r e s s u r e a r e produced on t h e f i l m from Chese p u l s e s o f l i g h t .
The d i s c r i m i n a t o r s were a d j u s t e d s o t h a t t h e h y s t e r e s i s would be a s
( 7 ) s m a l l a s p o s s i b l e
.
The h y s t e r e s i s i t s e l f g u a r a n t e e s t h a t t h e Ychmitt d i s c r i m i n a t o r w i l l o p e r a t e i n a s t a b l e manner. It i s p o s s i b l e , o f c o u r s e , t o make i t v e r y s m a l l , b u t t h e n a d a n g e r a r i s e s t h a t even a v e r y s l i g h t d i s t u r b a n c e of t h e i n p u t v o l t a g e would r e s u l t i n a n u n i n t e n t i o n a l r e v e r s a l . Moreover., a n o t h e r r e s u l t o f r e d u c i n g t h e h y s t e r e s i s i s t h a t t h e anode v o l t a g e jumps becomes m a l l e r and s m a l l e r , and f i n a l l y r e a c h 0 . On t h e o t h e r hand, by s u i t a b l e s e l e c t i o n of t u b e s and of t h e c o r r e c t o p e r a t i n g p o i n t , t h e h y s t e r e s i s c a n be r e d u c e d w i t h o u t t h e above-mentioned d i s t u r b i n g p r o p e r t i e s . The c i r c u i t was c h o s e n s o t h a t t h e h y s t e r e s i s would be l e s s t h a n 100 mv f o r a r e s p o n s e v o l t a g e o f 2 . 5 v . The r e s u l t i n g e r r o r i s l e s s t h a n 24% o r 2 0 .j d b . :Je s h a l l have more t o s a y below a b o u t t h e e f f e c t s of t h i s .
The change of r e s p o n s e l e v e l d u r i n g t h e e x p o s u r e t i m e i s l e s s t h a n 0 . 0 5 db, and i s t h u s n e g l i g i b l e .
The p u l s e s a r e formed by d i f f e r e n t i a t i o n of t h e anode v o l t a g e jumps. ,le now g e t a diagram I n which t h e sound f i e l d would be c h a r a c t e r i z e d by l i n e s of e q u a l sound p r e s s u r e . However, i t would be i m p o s s i b l e t o d i s t i n g u i s h w h e t h e r a g i v e n l i n e , which owing t o a n e q u a l i m p u l s e l e v e l p r o d u c e s e q u a l b l a c k e n i n g o f t h e f i l m , would r e p r e s e n t a n i s o b a r o f h l g h e r o r lower sound l e v e l t h a n t h e a d j a c e n t l i n e . F o r t h i s r e a s o n t h e i m p u l s e l e v e l o f t h e
discriminator o u t p u t v o l t a g e was v a r i e d i n s u c h a way t h a t t h e o u t p u t p u l s e o f t h e f i r s t d i s c r l m i n a t o r , which r e s p o n d s t o t h e s m a l l e s t v o l t a g e and hence g e n e r a t e s t h e 0 d b i s o b a r , r e c e i v e s t h e l o w e s t i ~ p u l s e l e v e l . I n t h e
l i n e . The p u l s e s of t h e remaining d i a c r i m i n a t o r s a r e s t a g e d i n such a way t h a t d i s c r i m i n a t o r
6,
which g e n e r a t e s t h e 25 db i s o b a r , h a s t h e g r e a t e s t a m p l i t u d e , which i n t u r n modulates t h e maximum p e r m i s s i b l e lamp c u r r e n t and t h u s t r a c e s t h e b r i g h t e s t and t h i c k e s t l i n e .F i g u r e
5
shows a n o s c l l l o g r a m which g i v e s t h e microphone v o l t a g e a t t h e t o p and t h e lamp c u r r e n t i n amplitude r e p r e s e n t a t i o n below. The s t a g i n g of t h e p u l s e l e v e l s i s c l e a r l y r e c o g n i z a b l e . A t t h e r i g h t and a t t h e l e f t of t h e photograph i t w i l l be s e e n t h a t some impulses come i n r a p i d s u c c e s s i o n and some o v e r l a p . T h i s i s because t h e d e c r e a s e of microphone v o l t a g e a tc o m p a r a t i v e l y g r e a t d i s t a n c e does not o c c u r c o n t i n u o u s l y owing t o r e f l e c t i o n s . The f a c t t h a t t h e impulses a r e n o t symmetrical w i t h r e s p e c t t o t h e peak of t h e microphone v o l t a g e w i l l be dLscussed below i n g r e a t e r d e t a i l i n c o n n e c t i o n w i t h t h e diagram e r r o r s .
The a v a i l a b l e b i t s of i n f o r m a t i o n ( i m p u l s e s of t h e amplitude channel, t h e f i l t e r e d and a m p l i f i e d microphone v o l t a g e , and t h e phase-locked comparison v o l t a g e ) a r e s u i t a b l y mixed and a m p l i f i e d i n mixing and o u t p u t a m p l i f i e r s , and a r e fed t o t h e lamp.
2
-4.
E l e c t r l c a l - o p t i c a l p a r tThe s i g n a l s , which flow through t h e o u t p u t t u b e i n t h e form of impulses and p u l s a t i n g d i r e c t c u r r e n t , must be converted i n t o an e q u i v a l e n t l i g h t beam. The lamp must meet v a r i o u s r e q u i r e m e n t s , of which t h e most i m p o r t a n t a r e t h e f o l l o w i n g :
1. The lamp must be s u b j e c t t o modulation of i t s b r i g h t n e s s w i t h l i t t l e i n e r t i a . Ey l i t t l e i n e r t l a y w e mean h e r e t h a t e v e r y d e t a i l of t h e sound f i e l d s t r u c t u r e should be imaged w i t h o u t d i s t o r t i o n a t a s c a n n i n g speed of approximately 1 . 3 m / s . I n c o n v e r t i n g t h e p u l s e s , t h e aim must be t o
have a p u l s e recorded a s a p o i n t , w i t h t h e r e s u l t t h a t a t h i n l i n e w i l l a p p e a r i n t h e f i g u r e when t h e p o i n t s a r e p u t t o g e t h e r . The luminous d u r a - t i o n should t h e r e f o r e be such t h a t d u r i n g t h e movement of t h e lamp i t w i l l i l l u m i n a t e a p a t h o n l y of approximately 1 m m . Referred t o t h e time, t h i s means t h a t a l i g h t p u l s e of approximately 0.8 m s d u r a t i o n must be produced. The t o p l i m i t i n g f r e q u e n c y must t h e r e f o r e be g r e a t e r t h a n 1 k c .
T h i s e l i m i n a t e s a l l i n c a n d e s c e n t lamps, even t h o s e t h a t a r e p r e h e a t e d and have v e r y t h i n f i l a m e n t s .
2 . The second requirement r e l a t e s t o s u s c e p t i b i l i t y t o modulation. The l i g h t s o u r c e must have a s g r e a t a s p o s s i b l e a range of modulation. Between t h e two b o u n d a r i e s g i v e n by t h e p e r m i s s i b l e l o a d o r a c c e p t a b l e overload (100%
modulation) and t h e unloaded s t a t e (modulation
o$),
t h e r e must be al i g h t i n t e n s i t y on t h e o t h e r .
3 . The l i g h t i n t e n s i t y o f t h e lamp must b e g r e a t enouch s o t h a t even a f t e r t a k i n g a l l l o s s e s i n t o a c c o u n t t h e i l l u m i n a t i o n i n t e n s i t y on t h e p h o t o - g r a p h i c f i l m i s s u f f i c i e n t l y g r e a t t o produce a d e q u a t e b l a c k e n i n g .
4. The l i g h t s o u r c e must be p o i n t shaped and b e a s s m a l l a s p o s s i b l e , s i n c e i t must be s i t u a t e d i n t h e v i c i n i t y o f t h e sound f l e l d t h a t i s b e i n g s c a n n e d .
Requirements 1
-
3 a r e met by t h e Ozram 767740 p o i n t s o u r c e glow lamp. ?'he lanip i s 1 = 8 0 mm l o n g , w i t h a d i a m e t e r of d = 25 mm, \ l i t h t h e s ed i m e n s i o n s i t i s i m p o s s i b l e t o mount t h e lamp on t h e t i p o f t h e p r o b e . A
s e c o n d a r y e m i t t e r must t h e r e f o r e be p r o v i d e d . 2 . 5 . P h o t o g r a p h i c r e c o r d i n g and imaging e r r o r s
From t h e p h o t o g r a p h i c p o i n t of vlew, t h e aim i s t o g e t a l i g h t d i s t r i -
b u t i o n c u r v e of t h e e m i t t e r which w i l l e n s u r e a u n i f o r m e x p o s u r e o f t h e f i l m
i n r e l a t i o n t o t h e s o l i d a n g l e .
A c c o r d i n g l y , t h e r e f o r e , t h e l i g h t beam should b e g u i d e d s o t h a t t h e
d i v e r g e n t r a d i a t i o n from t h e lamp i s a t f i r s t c o l l e c t e d , i s conducted p a r a l l e l t o t h e p r o b e a s f a r a s t h e t i p , and t h e n s t r i k e s t h e s e c o n d a r y e m i t t e r , which p r o v i d e s f o r t h e d e s i r e d d i s t r i b u t i o n i n s p a c e . For t h e e m i t t e r a s m a l l plane-convex l e n s a b o u t 8 mm i n d i a m e t e r i s u s e d , w i t h t h e s u r f a c e of t h e p l a n e s i d e roughened s o a s t o a c t as a ground g l a s s s c r e e n and c a u s e a d d i - t i o n a l s c a t t e r i n g .
T h i s l i g h t beam c o n v e r s i o n i s n o t v e r y e f f i c i e n t . T h e r e f o r e maximum p h o t o g r a p h i c s e n s i t i v i t y , 1 . e . a f a s t o b J e c t i v e and f i l m m a t e r i a l o f t h e h i g h e s t s e n s i t i v i t y , must be u s e d . We employed Agfa Rekord f i l m , which c a n be pushed t o a b o u t 36/10 D I N .
The l a g between t h e a c o u s t i c a l measurement a t t h e p r o b e t i p and t h e o p t i c a l s i g n a l c a u s e s a d i s t o r t i o n e q u a l t o t h e d i s t a n c e t h r o u g h which t h e microphone and lamp have moved i n t h e same p e r i o d .
The l a g A t
i s
a b o u t 1 0 m s , and c o m p r i s e s t h e t i m e t a k e n by t h e sound t o t r a v e r s e t h e p r o b e , t h e t i m e t a k e n t o i n i t i a t e t h e f i l t e r s , and t h e t i m e c o n s t a n t of t h e rectifier c i r c u i t . Added t o t h i s is t h e h y s t e r e s i s e r r o r i n t h e a m p l i t u d e r e p r e s e n t a t i o n , which a c t s a s a n a p p a r e n t l a g .The r e s u l t i n g imaging e r r o r c a n b e e l i m i n a t e d i n a s i m p l e manner, by d i s p l a c i n g t h e p o s i t l o n of t h e o p t i c a l image ( t h e ground g l a s s p l a n e a t t h e t i p of t h e p r o b e ) a d i s t a n c e c o r r e s p o n d i n g t o t h e l a g t i m e ( a b o u t 13 mm). The l i g h t s i g n a l i s t h e n r e c o r d e d a t t h e p o s i t i o n a t which t h e p r o b e a x i s was s i t u a t e d 10 m s e a r l i e r .
T h i s assumes, of c o u r s e , t h a t . A t i s c o n s t a n t , a c o n d i t i o n t h a t a p p l i e s o n l y t o t h e phase r e p r e s e n t a t l o n . The e r r o r which a r i a e s i n t h e amplitude r e p r e s e n t a t i o n owing t o t h e h y s t e r e s i s of t h e d i a c r l . m i n a t o r s , Is not s o e a s i l y t a k e n c a r e o f . ble s h a l l t h e r e c o r e i n v e n t i g a t e i t b r i e f l y . A s a l - r e a d y mentioned, t h e h y s t e r e s i s i s 0 .j d b . For an i n c r e a s i n g microphone v o l t a g e , t h e itnpulse f o r producing t h e I s o b a r s i s o n l y g i v e n when t h e c o n t r o l v o l t a g e i s +0.3 dL. above tF:e r a t e d v a l u e , I n t h e c a s e of d r o p p i n g v o l t a g e t h e impulse i s generated a t - 0 . 3 d b . I f w e a g a l n c o n s i d e r F i g .
5,
where t h e microphone v o l t a g e , owing t o t h e co!?stant scanning s p e e d a n d t h e p o i n t form of t h e sound s o u r c e f o l l o w s a symmetrical curve, two f a c t s ~ I l l berecognized :
1. The h y s t e r e s i s c a u s e s both Sinpulses of a s t a g e t o be " t o o l a t e " by t h e same amount on account of t h e symmetry of t h e v o l t a g e c u r v e . A s a
consequence a n a d d i t i o n a l a p p a r e n t l a g i s brought a b o u t , which however can be c o r r e c t e d by displacement of t h e o p t i c a l image, s o t h a t t h e v a l u e of 2 0 . 3 db f o r t h e h y s t e r e s i s Ls not i d e n t i c a l w i t h t h e u n c e r t a i n t y involved
i n t h e i s o b a r diagram.
2 . The magnitude of t h e a p p a r e n t l a g depends on t h e s t e e p n e s s of t h e v o l t a g e I n c r e a s e o r d e c r e a s e a s t h e c a s e may b e . d U / d r i n g r e a t e s t i n t h e v i c i n i t y of t h e e m i t t e r and hence t h e d i s t o r t i o n caused by t h e h y s t e r e s i s i s
s m a l l e s t h e r e . ' d i t h I n c r e a s i n g d i s t a n c e t h e s t e e p n e s s d e c r e a s e s and t h e r e c o r d i n g e r r o r becomes g r e a t e r . Assuming a ~ / r curve of sound p r e s s u r e , and drawing t h e i s o b a r s f o r t h e maximum l e v e l , f o r example, s o t h a t
5
=1 . 5 cm, t h e n t h e i s o b a r s of t h e lowest l e v e l w i l l be
= 27 cm (-25 d b ) .A t t h i s d i s t a n c e t h e s t e e p n e s s I s approximately 0 . 3 db/cm, w i t h which t h e displacement a t t a i n s a v a l u e of approximately 1 cm. T h e o r e t i c a l l y t h i s e f f e c t would be r e c o g n i z a b l e i n t h e sound f i e l d p i c t u r e s , however i t h a s been found t h a t a t t h i s d i s t a n c e a c o u s t i c a l d i s t u r b a n c e s a l r e a d y predomi- n a t e , a s i s shown i n t h e n e x t s e c t i o n . I n t h e v i c i n i t y of t h e e m i t t e r , however, t h e e r r o r i s compensated by t h e displacement of t h e o p t i c a l image.
N e v e r t h e l e s s a s l i g h t i n a c c u r a c y remains, s i n c e t h e t o t a l l a g t i m e f o r t h e amplitude record i s a few milliseconds g r e a t e r t h a n f o r t h e phase r e c o r d . The d i s t o r t i o n , c a n t h e r e f o r e , amount t o a ferr m i l l i m e t r e s , b u t i n most c a s e s t h i s I3 e n t i r e l y unimportant, s i n c e t h e d i s c r e p a n c y i n t h e p i c t u r e s can no l o n g e r be r e c o g n i z e d .
The o p t i c a l imaging of a sound f i e l d i s f u r t h e r supplemented by t h e s u p e r p o s i t i o n of a system of c o o r d i n a t e s ( g r i d l i n e s 1 0 cm a p a r t ) .
3.1. Sound f i e l d r e c o r d s of a s p h e r i c a l e m i t t e r
The s i r n p l e s t c a s e i s t h a t of ~ ~ n n i d l r e c t i o n a l t-mission of t h e t y p e
produced by a s p h e r i c a l e m i t t e r o f z e r o t h o r d e r . The i n d i v i d u a l elements of t h e s u r f a c e o f t h e s p h e r e h e r e o s c i l l a t e w i t h c o n s t a n t v e l o c i t y a m p l i t u d e , outwards and i n w a r d s i n p h a s e . The o o ~ n d f l e l d of such an emmiter i s c h a r a c t e r i z e d by t h e f a c t t h a t b o t h t h e s u r f a c e s of e q u a l phase and t h e s u r f a c e s of e q u a l sound p r e s s u r e arnplitude a r e c o n c e n t r i c s p h e r e s w i t h t h e e m i t t e r a s a comlnon c e n t r e . P r a c t i c a l l y , an e m i t t e r of z e r o t h o r d e r i n t h e form of a d i l a t i n g s p h e r e 1s u n r e a l i z a b l e .
For t h e t e s t s a miniature magnetic earphone was used which had t h e f o l l o w i n g dimensions: diarneter 20 mm, h e i g h t 11 mm and d i a m e t e r of sound- e m i t t i n g a p e r t u r e 2 rnm. For t h e lower f r e q u e n c i e s a s p h e r i c a l c h a r a c t e r i s t i c
i s
indeed o b t a i n e d , b u t t h e amount r a d i a t e d i s v e r y s m a l l .For sound f i e l d r e p r e s e n t a t i o n a s e c t i o n i s c u t t h r o u g h t h e f i e l d . I n . t h e p r e s e n t c a s e t h e s c ( : t i o t ~ L Y b e s t talcen t h r o u g h t h e o r i g i n . Owing t o t h e f i n i t e dimensions of t h e c t n i t t e r , of c o u r s e , t h i s can not be e x a c t l y r e a l i z e d i n t h e p r e s e q t c a s e , b u t t h e d e p a r t ~ r e s from i t a r e v e r y small. The d i s t a n c e betvreen t h e e m i t t e r and t h e probe t i p of' t h e microphone was about 10 mm.
I n t h e sound f i e l d r e p r e s e n t s ' i i o n t h e c u r v e s o f c o n s t a n t phase produce c o n c e n t r i c c i r c l e s whose d i s t a L ~ c e a p a r t i s e q d a l t o t h e wavelength. For making t h e r e c o r d ( ~ i g . 6 ) a f r e q u e n c y of f =
3 . 4
k - was chosen. The wave-l e n g t h i s t h e n h = 13 cm.
The l i n e s of e q u a l sound l e v e l , t o be s u r e , a l s o form c o n c e n t r i c c i r c l e s b u t t h e i r d i s t a n c e a p a r t i s not c o n s t a n t . T h e y v a r y i n accordance w i t h t h e law of p r o p a g a t i o n . I n t h e s p h e r i c a l wave t h e sound p r e s s u r e d e c r e a s e s c o n t i n u o u s l y (even i n t h e n e a r f l e l d ) a t t h e r a t e l/r. The s i x i s o b a r s a r e r e c o r d e d i n
5
db s t a g e s of t h e sound l e v e l . Denoting t h e i s o b a r s s o t h a t i s o b a r 1 i s a s s i g n e d t o t h e r e l a t i v e sound l e v e l 0 db, i s o b a r 2 t o l e v e l5
d b , t h e n i s o b a r 6 c o r r e s p o n d s t o t h e l a r g e s t l e v e l L, = 25 db. I n T a b l e I t h e sound l e v e l s L, t h e sound p r e s s u r e a m p l i t u d e s p and t h e c o r r e s p o n d i n g f i e l d p o i n t i n t e r v a l sr ,
a s o b t a i n e d from t h e l/r law, a r e g i v e n f o r t h e s i x i s o b a r s .Novr c o n s i d e r i n g F i g . 7, xrhich sholv~s t h e sound d i s t r i b u t i o n of t h e f i e l d f o r t h e f r e q u e n c y f = 4 . 0 kc, we a g a i n s e e t h e expected c o n c e n t r i c c i r c l e s i n t h e v i c i n i t y of t h e e m i t t e r . l l i t h i n c r e a s i n g d i s t a n c e , t h e c u r v e s g r a d u a l l y l o s e t h e i r c i r c u l a r shape, and a r e s u b j e c t t o wavy i n d e n t a t i o n s . I n a d d i t i o n , i n d i v i d u a l i s l a n d s form between t h e concentric c u r v e s .
s t r i k e u s as anomalous, b u t a r c e a s y t o e x p l a i n . The s p a c e i n which t h e r e c o r d s a r e b e i n g made, al.tl?ougtl v e r y s t r o n g l y damped w i t h r e s p e c t t o s o u n d ,
i s n o t t o t a l l y f r e e from r e f l e c t i o n s . Even i f i t w e r e , some i n t e r f e r i n g r e f l e c t i o n s c o u l d n o t b e entirely a v o i d e d , s i n c e t h e a p p a r a t u s r e q u i r e d f o r t h e measurement must b e s i t u a t e d i n t h e v i c i n i t y o f t h e f i e l d t o be investigated. I n what f o l l o w s , t h e sound f i e l d r e c o r d s a r e t o b e q u a n t i t a t i v e l y e v a l u a t e d . I t w i l l t h e n be p o s s i b l e t o s a y something a b o u t t h e o r d e r o f magnitude of t h e i n t e r f e r e n c e s o b s e r v e d . I t w i l l be t h e a i m o f t h i s e v a l u a - t i o n t o d e t e n n i n e vrhether t h e sound ernission i s s p h e r i c a l . A t t h e g i v e n f r e q u e n c y f = 4 k c t h e r a t i o d / h = l / 4 . 2 5 i s o b t a i n e d . l l i t h t h i s o n l y a
s l i g h t d e p a r t u r e from t h e s p h e r i c a l c h a r a c t e r i s t i c i s e x p e c t e d .
For t h e e v a l u a t i o n d i a m e t e r s TI, t o D, of t h e r e c o r d e d i s o b a r s a r e m e a s u r e d . I n t h e c a s e of t h e no l o n g e r c i r c u l a r c u r v e s , t h e extreme v a l u e s Drnax and Drnin a r e d e t e r m i n e d . These v a l u e s a r e e n t e r e d I n columns
3
and 4 of T a b l e 11. The mean v a l u e s D d e t e r m i n e d from t h i s a r e g i v e n i n columnmean
5 .
\ J i t h t h e a i d o f t h e 1 0 cm g r i d , t h e s c a l e o f r e d u c t i o n M f o r t h e d i a g r a mi s d e t e r m i n e d . M u l t i p l y i n g t h e v a l u e s f o r Dmean by 111/2, we g e t t h e r a d i i r '
i n t h e image p l a n e (column 6 ) . For s m a l l r a d i i r ' a c o r r e c t i o n must be
a p p l i e d -;:hich t a k e s i n t o a c c o u n t t h e d i s t a n c e a between t h e e m i t t e r and t h e t i p of t h e p r o b e . T h e d i s t a n c e r s o u g h t b e t w e e n f i e l d p o i n t s i s t h e
h y p o t e n u s e of a t r i a n g l e , t h e b a s c s o f 1;ihich a r e t h e r a d i u s
r 1
and t h e d i s t a n c e a . Accordin[; t o t h e Pythagoilean theorem, t h e nThe d i s t a n c e s r b e t x e e n f i e l d p o i n t s t h u s c a l c u l a t e d a r e e n t e r e d i n column 7 .
F o r t h e s e p o i n t s l:~e c a l c u l a t e d t h e sound l e v e l v a l u e s L o b t a i n e d from t h e
l/r l a w . It i s b e s t t o choose a r e f e r e n c e p o i n t i n t h e c e n t r a l r e g i o n , s i n c e t h a t l v r i i l g i v e t h e most a c c u r a t e v a l u e . Yor t h e p r e s e n t example t h e r a d i u s of t h e i s o b a r 4 -!as c h o s e n a s r e f e r e n c e . I n column 3 t h e sound l e v e l s Lcalc a r e e n t e r e d . The d i f f e l p e n c e between L c a l c
.
and L i s e n t e r e d a s a mean d e v i a t i o n i n colulnn9.
Ass~.imln& a r e n d i n g a c c u r a c y of 2 0 . 5 mm,t h e n :;re g e t t h e u n c e r t a i n t i e s g i v e n i n column 1 0 , r e f e r r e d t o t h e sound l e v e l . The w a v i n e s s of thc i s o b a r s a t a [;?-eater d i s t a n c e i.s a consequence o f l e v e l
f l u c t u a t i o n s , :.rh!.ch a r e s i v e n i n tihe l a s t column.
C o n s i d e r i n g t h e mean e r r o r s :Ln column 9, i t w i l l b e r e c o g n i z e d t h a t t h e l a t t e r i n c r e a s e from -0.9 d b ( i s o b a r 1) t o + l . 1 db ( i s o b a r 6 ) . The d r a w i n g o f t h e i s o b a r s t h e m s e l v e s u n t a l l s a n u n c e r t a i n t y of a b o u t 5 0 . 3 d b , made up of t h e e r r o r o?rl.n~ t o t h e hysteresis of t h e discriminators and t h e c a l i b r a t i o n of t h e r e s p o n s e v o l t a g e . E v e n ~ r h e n a l l p o 3 s : l b l e sourlccs of e r r o r h a v e been
t a k e n i n t o a c c o u n t , a p a r t of t h e mean e r r o r s k i 1 1 remains i n t h e s e n s e t h a t t h e drop i n t h e l e v e l i s s t e e p e r t h a n g i v e n by l/r. Thus t h e requirement w i t h r e s p e c t t o t h e s p h e r i c a l c h a r a c t e r i s t i c Is n o t wholly s a t i s f i e d . The d i r e c t i o n of t h e p r e f e r r e d sound e m i s s i o n i s p e r p e n d i c u l a r t o t h e p l a n e of
s c a n n i n g , o r , seen from t h e p o s i t l - o n of t h e earphone, I s i n t h e d i r e c t i o n of t h e sound-emission a p e r t u r e .
The s t r i k i n g l y wavy c h a r a c t e r of t h e more d i s t a n t i s o b a r s i s a conse- quence of f l u c t u a t i o n s of l e v e l amounting t o t0.8 db i n t h e v i c i n i t y of i s o b a r 1 and 5 0 . 6 db n e a r i s o b a r 2 . I n themselves t h e s e f l u c t u a t i o n s a r e s l i g h t and would s c a r c e l y c a u s e any i n t e r f e r e n c e f o r most p r a c t i c a l measure- ment p u r p o s e s i n t h e sound f i e l d . The f a c t t h a t t h e y a p p e a r so prominently
i n sound f i e l d photography l i e s f i r s t of a l l i n t h e n a t u r e of t h e l/r
d e c r e a s e and secondly i n t h e e x a c t c h a r a c t e r of t h e r e p r o d u c t i o n method, which shows e v e r y d e t a l l of t h e f i e l d . I n o r d i n a r y g r a p h i c a l r e p r e s e n t a t i o n of f i e l d s , determined by p o i n t - b y - p o i n t measurement, t h e s e f i n e d e t a i l s cannot be brought o u t . The same a p p l i e s t o t h e i s l a n d s a p p e a r i n g i n t h e p i c t u r e s .
S i n c e t h e e v a l u a t i o n showed t h a t f o r t h e m i n i a t u r e earphone and a
frequency f = 4.0 kc d e p a r t u r e s from t h e s p h e r i c a l c h a r a c t e r i s t i c were s t i l l measurable, an a t t e m p t was made t o r e a l i z e t h e s p h e r i c a l e m i t t e r i n a n o t h e r manner. F o r t h i s purpose a t h i n p i p e having a n o u t s i d e d i a m e t e r of 6 mm
and a l e n g t h of 1 metre was used f o r sound t r a n s m i s s i o n . A m i n i a t u r e e a r - phone i s coupled t o one end of t h e t u b e w h i l e t h e o t h e r end p r o j e c t s a s a probe i n t o t h e sound f i e l d . For t h e f r e q u e n c y f E 4 k c , we t h u s g e t a r a t i o
Conlpared t o t h e f i r s t t e s t t h e v a l u e i s reduced by 1/3.
F i g u r e 8 shows t h e sound r e c o r d of t h i s s e t - u p . The e v a l u a t i o n i s c a r r i e d o u t i n T a b l e 111. The mean e r r o r l i e s between 0 and -1-0.4 d b . With a n u n c e r t a i n t y of 5 0 . 2 db t h e l e v e l d e c r e a s e c o r r e s p o n d s t o t h e expected l/r r e l a t i o n s h i p . In comparing t h i s w i t h t h e sound p i c t u r e of F i g . 7 i t i s noted t h a t t h e d e p a r t u r e s from t h e c i r c u l a r shape of t h e i s o b a r s a r e g r e a t e r i n F i g .
8,
a s t h e e v a l u a t i o n ( l a s t column, T a b l e 111) a l s o i n d i c a t e s . Whereas i n F i g . 7 t h e4
i n n e r i s o b a r s a r e p r a c t i c a l l y c i r c u l a r , i n F i g .8
o n l y t h e two innermost a r e u n d i s t o r t e d . The magnitude of t h e l e v e l f l u c t u a t i o n a s a f u n c t i o n of t h e d i s t a n c e f o l l o ~ ~ s d i f f e r e n t c o u r s e s i n t h e two c a s e s . Accord- i n g t o Table 111 ( t h e p i p e ) !.Je g e t a f l u c t u a t i o n of t0.8 t o 2 0 . 9 db f o r i s o b a r s 1 t o3 ,
n h e r e a s w i t h t h e m i n i a t u r e earphone t h e d i s t o r t i o n becomes g r e a t e r w i t h i n c r e a s i n g d i s t a n c e . Presumably t h i s e f f e c t depends on t h e f a c tt h a t t h e p i p e I t s e l f c o r i t r l b u t e s t o t h e sound c r n l s s i o r ~ , s o t h a t ari l n t e r - f e r e n c e f i e l d i s formed. E f f e c t i v e i n s u l a t t o n of t h e p i p e l ~ ~ o u l d r e a u l t i n an i n c r e a s e of d i a m e t e r , which i n t u r n would lricraease t h e r a t i o d / h .
For a broad c l a s s of experiments i n whLch s p h e r i c a l e m l t t e r s were
needed, t h e r e f o r e , m i n i a t u r e earphones were employed, sPnce t h e s e do n o t cause any a d d i t i o n a l sound f i e l d distortions and s a t i s f y t h e s p h e r i c a l
c h a r a c t e r i s t i c requirement approxlrnately.
To conclude t h e s e remarks, two additional p o i n t s may be mentioned:
1. The e v a l u a t i o n of i s o b a r s i n t h e immediate v i c i n i t y of t h e e m i t t e r i s n o t always p o s s l b l e v ~ i t h l n t h e s p e c i f i e d u n c e r t a i n t y of measurement. For one t h i n g , t h e d e t e r m j n a t i o n of t h e d i s t a n c e a between e m i t t e r and r e c e i v e r i s not always u n e q u i v o c a l , and, f o r a n o t h e r , we cannot be c e r t a i n whether i n e v e r y c a s e t h e p r o p a g a t l o n of t h e sound c a n be r e - garded a s u n d i s t o r t e d , i f t h e mlcrophone probe a p e r t u r e i s v e r y c l o s e t o t h e e m i t t e r .
2 . The i s o b a r c u r v e s a r e a s a r u l e i n t e r r u p t e d o r broken i n two p l a c e s . T h i s i s a minor l a c k of r e f i n e m e n t , due t o t h e f o l l o w i n g c a u s e s :
During t h e time t h e microphone i s moving a l o n g an i s o b a r , i . e . i s n o t I n t e r s e c t i n g i t , t h e c o n t r o l v o l t a g e of t h e d i s c r i m i n a t o r involved remains c o n s t a n t . I f t h e r e s p o n s e v o l t a g e i s n o t exceeded, t h e n t h e d i s c r i m i n a t o r cannot d e l i v e r a p u l s e . The consequence i s t h a t d u r i n g t h i s t i m e r e c o r d i n g i s i n t e r r u p t e d . The scanning of t h e f i e l d t a k e s p l a c e i n t h e v i c i n i t y of t h e e m i t t e r i n a n approximately p e r p e n d i c u l a r d i r e c t i o n . The f i g u r e s show t h a t a t p l a c e s where t h e i s o b a r s a r e touched p e r p e n d i c u l a r l y , t h e r e c o r d i s b r i e f l y i n t e r m p t e d
.
3 . 2 . The group of two s e p a r a t e e m i t t e r s
I n t h i s s e c t i o n a number of e x p e r i m e n t a l l y o b t a i n e d sound f i e l d r e c o r d s a r e c o n t r a s t e d w i t h g r a p h i c a l r e p r e s e n t a t i o n s of c a l c u l a t e d f i e l d s , a s
(81 p r e s e n t e d by S t e n z e l and Brosze +
I n t h e n e a r f i e l d , t h e group of two i n d i v i d u a l e m i t t e r s shoxs v e r y complex f i e l d s t r u c t u r e . I n t h e t h e o r e t i c a l r e p r e s e n t a t i o n of t h e f i e l d it i s n e c e s s a r y t o c a l c u l a t e a m u l t i p l i c i t y of p o i n t s i n o r d e r t o be a b l e t o review t h e e n t i r e field by i n t e r p o l a t i o n . Moreover i t i s n e c e s s a r y t o c a r r y on a s e p a r a t e c a l c u l a t i o n f o r each r a t i o d / h ( g e o m e t r i c a l e l o n g a t i o n t o t h e w a v e l e n g t h ) . S t e n z e l , t h e r e f o r e , confined himself t o a number of s p e c i f i c
examples. The g r a p h i c a l r e p r e s e n t a t i o n of t h e c a l c u l a t e d f i e l d s i s c a r r i e d o u t , a s f o r t h e sound f i e l d photograph, by means of c u r v e s of c o n s t a n t sound p r e s s u r e amplitude and e q u a l phase i n t h e p l a n e of t h e e m i t t e r , which i s
p e r m i t s d i r e c t comparison between t h e r e s u l t s of t h e t h e o r e t i c a l c a l c u l a t i o n and t h e p r a c t i c a l r e s u l t s of measurement i n t h e forr;i of a sound f i e l d
photograph.
For t h e c a l c u l a t i o n of t h e f i e l d i t was assumed by S t e n z e l t h a t t h e two e m i t t e r s a r e of z e r o t h o r d e r , i . e . t h e i r dimensions a r e s m a l l compared w i t h t h e wavelength, and t h a t t h e d i s t a n c e between t h e two e m i t t e r s d = 2 h . The d i f f e r e n c e of i n i t i a l phase between t h e two e m i t t e r s i s denoted by Y , t h e r e l a t i o n s h i p between t h e two i n i t i a l a m p l i t u d e s by b .
I n t h e p r a c t i c a l e x e c u t i o n of t h e comparison two m i n i a t u r e magnetic e a r - phones, which b e a t meet t h e r e q u i r e m e n t s , were employed a s e m i t t e r s .
So t h a t t h e sound f i e l d photograph could be r e a d i l y compared w i t h t h e g r a p h i c a l r e p r e s e n t a t i o n , t h e phase d i s t r i b u t i o n and amplitude d i s t r i b u t i o n I n t h e f i e l d were recorded s e p a r a t e l y . A f r e q u e n c y of
6.8
kc was chosen f o r t h e phase p i c t u r e s , w h i l e t h e r e c o r d i n g of t h e sound-pressure amplitude was c a r r i e d o u t a t f = 3 . 4 k c . Here, owing t o t h e l a r g e r d i s t a n c e betweene m i t t e r s ( d = 2 h = 20 cm) a b e t t e r r e s o l u t i o n i s o b t a i n e d , because owing t o t h e i n t e r f e r e n c e f i e l d t h e i s o b a r s a r e very c l o s e t o each o t h e r . The en- l a r g e d segments were chosen s o a s t o correspond approximately t o t h e s c a l e o f S t e n z e l l s sound f i e l d r e p r e s e n t a t i o n .
The f o l l o w i n g c a s e i s i n v e s t i g a t e d :
Equal i n i t i a l amplitude ( b = l ) , same i n i t i a l phase ( y = 0 )
Sound f i e l d r e c o r d of phase F i g u r e
9
Sound f i e l d r e c o r d of amplitude F i g u r e 11For comparison: ( a f t e r 3 t e n z e l )
G r a p h i c a l r e p r e s e n t a t i o n of phase F i g u r e 10 G r a p h i c a l r e p r e s e n t a t i o n of amplitude F i g u r e 12
)[hen we compare t h e sound f i e l d r e c o r d s w i t h t h e t h e o r e t i c a l l y determined f i e l d p a t t e r n s , good agreement i s o b t a i n e d . However, t h e f o l l o w i n g p o i n t s must be borne i n mind :
S t e n z e l ' s r e p r e s e n t a t i o n s of t h e l i n e s of c o n s t a n t phase show c u r v e s s i t u a t e d c l o s e r t o g e t h e r t h a n t h o s e of t h e sound f1,eld r e c o r d s . I n t h e former c a s e t h e y a r e drawn w i t h an i n t e r v a l of ~ / 4 , w h i l e i n t h e photo-
graphs t h e i n t e r v a l i s 2a. There i s a l s o a d i f f e r e n c e i n t h e c u r v e s of e q u a l sound p r e s s u r e a m p l i t u d e . I n t h e photograph t h e i n t e r v a l between two l i n e s c o r r e s p o n d s t o a sound l e v e l d i f f e r e n c e of
5
db, hence g r a d a t i o n conforms t o a l o g a r i t h m i c s c a l e . S t e n z e l , however, shows a l i n e a r s c a l e . Here t h e sound p r e s s u r e a m p l i t u d e s 0 . 2 5 p , 0 . 5 p, 0 . 7 5 p, 1 . 0 p, 1 . 5 p and 2 . 0 p a r e a s s i g n e d t o t h e c u r v e s .I t cannot be e x p e c t e d , of c o u r s e , t h a t t h e sound f i e l d photographs w i l l
d i s t u r b a n c e s (waviness of t h e i s o b a r s ) must be expected t h a t were d e a l t w i t h i n t h e p r e c e d i n g s e c t i o n .
3 . 3 . I n v e s t i g a t i o n of a model b e l l
3 - 3 . l . I n t r o d u c t i o n
Having now d e a l t w i t h sound f i e l d s t h a t can e a s i l y be g r a s p e d , o r t h a t have a l r e a d y been c a l c u l a t e d , we now c o n s i d e r a n e m i t t e r whose complete sound p r o p a g a t i o n c o n d i t i o n s have not y e t been i n v e s t i g a t e d , namely t h e b e l l .
People t a l k , of c o u r s e , about t h e "tone1' of a b e l l . Frequency a n a l y s i s shows a l i n e spectrum: t h e t o n e i e made up of v a r i o u s i n d i v i d u a l t o n e s .
Each i n d i v i d u a l t o n e of t h e b e l l i s a c e r t a i n form of v i b r a t i o n , and is t h u s a s s o c i a t e d w i t h a s p e c i f i c sound f i e l d .
The f i r s t i n v e s t i g a t i o n s i n t o t h e v i b r a t i o n a l behaviour of t h e b e l l were made 100 y e a r s ago by H . v . Helmholtz. I n h i s book "The t h e o r y of
sound s e n s a t ions" ('), which appeared i n 1862, he wrote:
s he
u ~ u a l k i n d s of v i b r a t i o n s ( o f t h e b e l l ) a r e t h o s e i n which 4, 6,8 ,
10 e t c . nodal c u r v e s form which descend i n e q u a l i n t e r v a l s from t h e crown t o t h e rim.."v . Helmholtz had a l r e a d y recognized t h e e x i s t e n c e of nodal r i n g s : "Other b e l l v i b r a t i o n forms a r e a l s o p o s s i b l e , i n which nodal c i r c l e s form t h a t a r e p a r a l l e l t o t h e r i m ; however, t h e s e a p p e a r d i f f i c u l t t o produce and have not y e t been i n v e s t i g a t e d . I '
The o p t i c a l sound f i e l d r e p r e s e n t a t i o n of a model b e l l i s i n t e r e s t i n g from two p o i n t s of view. I n t h e f i r s t p l a c e i t g i v e s i n f o r m a t i o n concerning t h e composition of t h e t o t a l sound f i e l d from t h e f i e l d s of t h e i n d i v i d u a l p a r t i a l t o n e s . Secondly, it i s g e n e r a l l y p o s s i b l e without d i f f i c u l t y t o draw c o n c l u s i o n s concerning t h e v i b r a t i o n a l behaviour of t h e e m i t t e r . The method u s u a l l y employed h i t h e r t o t o i n v e s t i g a t e t h e i n d i v i d u a l v i b r a t i o n forms was t h e point-by-point scanning of t h e b e l l s u r f a c e w i t h v i b r a t i o n p i c k u p s .
3.3.2.
The r e c o r d i n g of t h e sound f i e l d sVhen s t r u c k w i t h a c l a p p e r a l l i n d i v i d u a l t o n e s of t h e b e l l a r e e x c i t e d s i m u l t a n e o u s l y and c o n t i n u e sounding i n accordance w i t h t h e i r damping. T h i s manner of e x c i t a t i o n i s not s u i t a b l e f o r t h e photographing o f t h e sound f i e l d . 'Ae must be c e r t a i n t h a t t h e sound f i e l d magnitudes remain c o n s t a n t f o r t h e e n t i r e r e c o r d i n g t i m e .
The b e l l was e x c i t e d t o s i n u s o i d a l v i b r a t i o n s by means of an e l e c t r o - mechanical c o n v e r t e r (phonograph r e c o r d c u t t i n g s y s t e m ) . It was t h u s
p o s s i b l e t o e x c i t e t h e e s s e n t i a l p a r t i a l t o n e s of t h e b e l l e f f e c t i v e l y . These a r e t o n e s of t h e f o l l o w i n g f r e q u e n c i e s : 1 . 4 kc, 3.35 k c , 3.7 k c , 4 . 7 kc,
For each p a r t i a l t o n e , t h r e e r e c o r d o were made a s f o l l o w s :
1. i n a p l a n e p a r a l l e l t;o t h e n x l s of sym~netr-y of t h e b e l l ( s i d e view of t h e b e l l ) * ;
2 . and j . i n p l a n e s p e r p e n d i c u l a r t o t h e a x i s of t h e b e l l , one below t h e mouth of t h e b e l l ( l o o k i n g down) and t h e o t h e r above t h e crown ( l o o k i n g U P )
I n a l l c a s e s t h e d i s t a n c e t o t h e o b j e c t of measurement was made a s small
a s p o s s i b l e , s o t h a t from t h e p o i n t of view of t h e o b s e r v e r t h e r e c o r d i n g p l a n e i s immediately behind t h e b e l l .
The model b e l l h a s a d i a m e t e r of
177
rnm, a h e i g h t of 142 mm and a weight of 3 . 2 k g .3 . 3 . 3 . E v a l u a t i o n
The e v a l u a t i o n s w i t h r e s p e c t t o t h e g i v e n form of v i b r a t i o n a r e c a r r i e d o u t a c c o r d i n g t o t h e f o l l o w i n g scheme:
The p l a n view of t h e b e l l from below g i v e s a n i d e a of t h e p o s i t i o n and number of nodal m e r i d i a n s . These can be determined b o t h from phase and a m p l i t u d e r e c o r d s . The f o l l o w i r g i s common t o a l l r e c o r d s : i n t h e phase r e c o r d s , r a d i a l l y d i s p o s e d zones of phase d i s c o n t i n u i t y can be r e c o g n i z e d . They d e t e r m i n e t h e number and p o s i t i o n of t h e n o d a l m e r i d i a n s . I n t h e r e g i o n of t h e phase d i s c o n t i n u i t y t h e sound p r e s s u r e a m p l i t u d e i s 0 , w h i l e t h e
maximum sound r a d i a t i o n o c c u r s o v e r t h e v i b r a t i o n b u l g e s . The sound i s o b a r s , t h e r e f o r e , y i e l d a p a t t e r n c i ~ a r a c t e r i z e d by l o b e s i n a s t e l l a r a r r a n g e m e n t . The number of l o b e s and t h e i r p o s i t i o n s determi.ae t h e v i b r a t i o n b u l g e s . F i g .
13 and F i g . 1 4 show examples of v i b r a t i o n forms w i t h d i f f e r e n t numbers
of n o d a l mel7idians ( 4 , 6 , 8 and 10).
The sound f i e l d r e c o r d s showing t h e s i d e of t h e b e l l y i e l d i n f o r m a t i o n on t h e l a t e r a l sound r a d i a t i o n , and t h u s on t h e a x i s t e n c e of n o d a l r i n g s
( ~ ' i g . 1 5 ) . Here t h e i n t e r p r e t a t i o n i s o f t e n some-rrhat more d i f f i c u l t . F i r s t
it i s n e c e s s a r y t o r e a l i z e once more t h a t t h e s e c t i o n a l p l a n e i s s i t u a t e d b e - hind t h e b e l l , t h e l o b e s which t r a v e l r a d i a l l y outward from t h e b e l l a r e t h u s s e c t i o n e d .
I n g e n e r a l , t h e sound r a d i a t i o n i s such t h a t two main r e g i o n s may be d i s t i n g u i s h e d . These a r e t h e components which a r e r a d i a t e d by t h e v i b r a t i n g w a l l of t h e b e l l ( a ) outward and ( b ) inward ( t o w a r d s t h e i n t e r i o r of t h e b e l l ) . I n view of t h e f i e l d c o n f i g u r a t i o n recorded i n t h e p l a n e of t h e
s e c t i o n , t h e s e r e g i o n s must b e d i s t i n g u i s h e d . The p a r t of t h e b e l l n e a r e s t t o t h e s c a n n i n g p l a n e y i e l d s t h e outwardly r a d i a t e d component o f t h e sound f o r
