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N A T U R W I S S E N S C H A F T E
H E R A U SG E G E B E N VON A R N O L D B E R L I N E R
U N T E R B E S O N D E R E R M I T W I R K U N G V O N H A N S S P E M A N N I N F R E I B U R G I. B R .
O R G A N D E R G E S E L L S C H A F T D E U T S C H E R N A T U R F O R S C H E R U N D Ä R Z T E
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H E F T 13 ( S E IT E 2 9 7 -3 2 0 ) 1. A P R I L 1 9 2 7 F Ü N F Z E H N T E R JAHRGANG
I N H U b er Sch allfeldp roblem e. V o n F e r d i n a n d
I r e n d e l e n b u r g , B erlin . (M it 8 F iguren) . . 297 B e r S alzsee M ar C h iq u ita in d er P ro v in z C ordoba
(Argentinien). V o n B . v . F r e y b e r g , H a lle a. S.
(M it 8 F i g u r e n ) ...304 Be s p r e c h u n g e n :
H a h n , O ., W a s le h rt uns die R a d io a k t iv itä t ü ber die G esch ich te der E rd e ? (R ef.: A . B orn, B e r l i n ) ...3 11 S c h m i e d e l , O., D as A lte r d er E rd e n ach dem
A b k ü h lu n g sp rozeß . (R ef.: A . B o rn , Berlin) 312 G u t e n b e r g , B ., D ie seism ische B oden un ru he
u nd ih r Z u sam m en han g m it den N a c h b a r
geb ieten , insbesondere G eologie u nd M ete
orologie. (R ef.: E . T am s, H am burg) . . . 313 N ö l k e , F r i e d r i c h , G eo tek ton isch e H yp oth esen .
(R ef.: A . P rey , Prag) ...313 J e n n y , H ., D ie alpine F altu n g . ( R e f.: R . P u rk ert,
G r a z ) ...314
A L T :
| S u e s s , F. E ., In tru sio n ste k to n ik und W an d e r
te k to n ik im variscisch en G rundgebirge. ( R e f.:
H an s B eck er, L e i p z i g ) ... 314 O b r u t s c h e w , W . A ., U b e r die S yste m a tik der
E rzla g e rstä tte n . (R ef.: J. L . W ilser, F re i
bu rg i. B r . ) ... 315 B u b n o f f , S e r g e v . , G eologie v o n E u ro p a.
B d . I. (R ef.: A . Born, B e r l i n ) ... 3 15 M i t t e i l u n g e n a u s v e r s c h i e d e n e n G e b i e t e n :
N eu e E rgebn isse ü ber die E n tw ick lu n g s
p h ysiolo gie des Insekten eies. D ie fun ktionelle V ersch ieden h eit der V ord er- und H in teraug en b ei N ereis. H erstellu n g v o n kü n stlich em K a u t sch u k in D eu tsch la n d w ähren d des W eltkrieges.
M itteilu n g en aus d en D eutsch en S ch utzgebieten . M eteorologische H ö h en statio n en in N orw egen.
D ie N a c h tig a ll in N orw egen . Z u r H e rk u n ft des G rund w assers. T h e corrosion of glass surface.
A rb eiten d er E rd m ag n etisch en A b teilu n g des C arn eg ie-In stitu ts in W ash in g to n 1925/26 . ^ 3 1 6
M a t e r ia l-P r ü fu n g e n
d u r c h R ö n t g e n s t r a h l e n
Eresco-Großeinrichtung- in einem technischen Betriebe
Rieh. S eifert & Co., H am burg 13
S p e zia lfab rik für R ö n tg en ap p arate
I I D I E N A T U R W I S S E N S C H A F T E N . 1927. H e ft 13. 1. April 1927.
DIE N ATURW ISSENSCHAFTEN
erscheinen w ö ch en tlich u nd kön n en im In - und A u sla n d e d u rch jed e S ortim e n tsb u ch h an d lu n g , jed e P o s t a n s t a lt od er den U n terzeich n eten V e rla g b e zo gen w erd en . P reis v ie rte ljä h rlic h fü r das In - und A u sla n d R M 9.— . H ie rzu t r it t bei d ire k te r Z u stellu n g d u rch den V e rla g das P o rto b z w . beim B e zü g e d u rch d ie P o s t die p osta lisch e B este llg e b ü h r. E in ze lh e ft R M 1.— zu z ü g lich P o rto .
M an u sk rip te, B ü c h e r usw . an
Die Naturwissenschaften, Berlin W 9, Linkstr. 23/24 erbeten.
P reis der In la n d -A n ze ig e n : 1/ 1 S eite R M 150.— ; M illim eter-Z eile R M 0.35. Z a h lb a r zu m am tlich en B erlin e r D o lla rk u rs am T a g e des Z ahlu n gsein gan g es.
F ü r V o rzu g sse ite n besondere V ere in b a ru n g . — B ei W ied erh o lu n gen N a c h la ß .
A u sla n d s-A n zeig en p reise w erd en a u f d irek te A n frag e m itg e te ilt.
K lisch e e-R ü ck se n d u n g en erfolgen zu L a s te n des Inseren ten .
Verlagsbuchhandlung Julius Springer, Berlin W 9, Linkstr. 23/24 Fernsprecher: A m t Kurfürst 6050— 53. Telegram m adr.: Springerbuch.
V e r l a g v o n J u l i u s S p r i n g e r i n B e r l i n W 9
S t r u k t u r d e r M a t e r i e
i n E i n z e l d a r s t e l l u n g e n
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D r. M. B o r n und D r. J. F r a n c k
Professor, D irektor des In stitu ts für th eo - Professor, D irektor des zw eiten physika- retische P h y sik der U niversität G öttingen lischen In stitu ts der U niversität G öttingen
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Mit 15 A bbildungen. VIII, 140 Seiten. RM 9.— ; g e b u n d e n RM 10.20 B i s h e r s i n d e r s c h i e n e n :
E r s t e r B a n d : Z e e m a n -E ffe k t und M ultiplettstruktur der Spektrallinien. V on Dr.
E. B a c k , P ri v a td o z e n t für E x p erim en talp h y sik an d e r U niv ers ität T ü b in g e n , u n d Dr. A. L a n d e , a. o. P r o f e s s o r für th e o r e ti s c h e P h y sik an d e r U niv ersität T ü b in g e n . Mit 25 T e x ta b b i ld u n g e n
un d 2 Tafeln. XII, 213 Seiten. 1925. RM 14.40; g e b u n d e n RM 15.90
Z w e i t e r B a n d : V o rle su n g e n über Atomm echanik. Von P r o f e s s o r Dr. M a x B o r n , D irektor d e s Instituts für th e o r e ti s c h e P h y s i k d e r U niv ersität G öttingen, u n te r Mitwirkung vo n Dr. F r i e d r i c h H u n d , P r i v a td o z e n t an d e r U niv ersität G öttingen. I. Band. Mit 43 A b
bildungen. IX, 358 Seiten. 1925. RM 15.— ; g e b u n d e n RM 16.50
D r i t t e r B a n d : A n r e g u n g von Q uan tensprü ngen durch Stöße. V on Dr. J. F r a n c k , P ro f e s s o r an d e r U n iv e rs itä t G öttingen, un d Dr. P . J o r d a n , A s siste n t am physikalischen Institut d e r U niv ersität Göttingen . Mit 51 A bbildungen. VIII, 312 Seiten. 1926.
RM 19.50; g e b u n d e n RM 21.—
Ein ausführlicher Prospekt steht Interessenten kostenlos zur Verfügung.
DIE NATURWISSENSCHAFTEN
F ü n f z e h n t e r J a h r g a n g x. A pril 1927 H e f t 13
Ü b e r S c h a l l f e l d p r o b l e m e 1).
V o n F e r d i n a n d T r e n d e l e n b u r g , B e r lin . (A us dem F orsch u n g sla b o ra toriu m in Siem ensstadt.) D e r e x p e r im e n te lle n U n te r s u c h u n g d e r rä u m -
J V fcn-<- ^ e r t e ^ u n g d e r B e s t im m u n g s s t ü c k e v o n ' 0 ^ e c ern w *e A m p lit u d e d e r s c h w in g e n d e n Ai t t e d c h e n , A m p lit u d e d e r T e ilc h e n g e s c h w in d ig k e it, u n d A m p lit u d e d e r D r u c k s c h w a n k u n g im le d iu m h a b e n s ic h b is h e r b e t r ä c h t lic h e S c h w ie r ig k e ite n e n t g e g e n g e s t e llt . E s w a r in s b e s o n d e re n u r sc h w e r m ö g lic h , q u a n t i t a t i v e M e s su n g e n in S c h a ll
fe ld e rn d u r c h z u fü h r e n . D ie F o r t s c h r it t e d e r e le k tr is c h e n M e th o d e n z u r K la n g u n t e r s u c h u n g h a b e n es j e t z t g e s t a t t e t , o b j e k t i v m e ss e n d in d ie S t r u k t u r r ä u m lic h a u s g e d e h n t e r S c h a llfe ld e r e in z u d r in g e n . D ie g e w o n n e n e n E r g e b n is s e k o n n te n in p h y s i
k a lis c h e m a b s o lu t e m M a ß a u s g e d r ü c k t w e rd e n . E s so lle n im fo lg e n d e n n a c h B e s p r e c h u n g d e s in n e re n Z u s a m m e n h a n g e s d e r g e n a n n te n a k u s t i sch en B e s tim m u n g s s t ü c k e e in e s S c h a llfe ld e s d ie M e th o d e n u n d d ie E r g e b n is s e v o n S c h a llf e l d m e ss u n g e n m it g e t e ilt w e rd e n .
Z u r E in le it u n g d e r t h e o r e t is c h e n B e t r a c h tu n g e n se ie n z u n ä c h s t d ie B e z ie h u n g e n d e r S c h a ll
fe ld g r ö ß e n u n t e r e in a n d e r u n d ih re B e z ie h u n g z u m C .G .S .- S y s t e m k u r z b e s p ro c h e n . E in e k la r e D e fin it io n a k u s t is c h e r G r u n d g r ö ß e n u n d d e r A n s c h lu ß d ie s e r G r ö ß e n a n d a s C .G .S .- S y s t e m is t ü b e r a ll d o r t v o n b e s o n d e r e r B e d e u t u n g , w o P r o b le m e b e h a n d e lt w e r d e n so lle n , w e lc h e a n G r e n z g e b ie t e n d e r A k u s t ik m it a n d e r e n W is s e n s z w e ig e n lie g e n , a ls o b e i
sp ie ls w e is e F r a g e n e le k t r o a k u s t is c h e r U m fo r m u n g . D e r A u s g a n g s p u n k t u n s e r e r Ü b e r le g u n g sei d e r B e g r i f f d e r S c h a lle is t u n g : e in e S c h a llq u e lle s t r a h lt in d e r Z e it e in h e it e in e b e s t im m t e E n e r g ie m e n g e in d a s S c h a llfe ld a b . D ie D im e n s io n d e r S c h a lle is t u n g is t d e m n a c h [l2m t ~3], g e m e ss e n w ir d d ie S c h a lle is t u n g in erg / se c = 10 “ 7 W a t t . D ie S c h a lls t r a h lu n g b r e i t e t s ic h im S c h a llfe ld a u s . A n e in e r b e s t im m t e n S t e lle d e s S c h a llfe ld e s t r i t t d e m n a c h e in e s e k u n d lic h e E n e r g ie m e n g e d u r c h d ie z u r I o rt p fla n z u n g s r ic h t u n g s e n k r e c h te F lä c h e n e in h e it, d ie s e S c h a lle is t u n g p ro c m 2 b e z e ic h n e t m a n a ls S c h a llin t e n s it ä t [ m r 3]. D a s M a ß d e r S c h a llin t e n s i t ä t is t erg / se c c m 2 = 10 _ 7 W a t t / c m 2. E s is t k la r, d a ß d ie S c h a llin t e n s it ä t e in e b e s o n d e rs w ic h tig e a k u s t is c h e G r ö ß e d a r s t e llt. S ie d e fin ie r t d en E n e r g ie t r a n s p o r t d u r c h d a s O b e r flä c h e n e le m e n t , a lle m it t e lb a r o d e r u n m it t e lb a r w a h r n e h m b a r e n
^ ir k u n g e n e in e s S c h a llv o r g a n g e s m ü sse n a ls o m it d e r S c h a llin t e n s it ä t a n d e r b e tr e ffe n d e n S te lle ln ir g e n d e in e r b e s t im m t e n V e r b in d u n g ste h e n .
E s se i n u n k u r z b e t r a c h t e t , in w e lc h e r W e is e d ie a) N a ch m einem V o rtr a g am 19. n . 26 in der gem ein samen S itzu n g der P h y sik a lisch e n G esellsch a ft zu B erlin Und der D eu tsch en G esellsch aft fü r tech n isch e P h y sik .
Nw. 1937
S c h a llin t e n s it ä t d u r c h d ie a n d e r e n a k u s t is c h e n S c h a llfe ld g r ö ß e n , n ä m lic h A m p lit u d e d e r s c h w in g e n d e n T e ilc h e n , T e ilc h e n g e s c h w in d ig k e it u n d A m p lit u d e d e r D r u c k s c h w a n k u n g im M e d iu m d a r s t e llb a r is t . F ü r d a s B e is p ie l d e r e b e n e n f o r t s c h r e ite n d e n W e lle sin d d ie s e Z u s a m m e n h ä n g e le ic h t zu ü b e rse h e n .
D ie S c h w in g u n g s fo r m e in e s s c h w in g e n d e n T e i l c h e n s se i:
a — a ' sin cot (t)
D a n n w ir d d ie I n t e n s i t ä t J
j = (2)
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= ( p T (4)
-j-p ' = e •u (5)
w o b e i g d ie D ic h t e , u d ie S c h a llg e s c h w in d ig k e it , v d ie T e ilc h e n g e s c h w in d ig k e it u n d p d ie D r u c k s c h w a n k u n g im M e d iu m b e d e u t e t . D ie A b le it u n g d ie s e r B e z ie h u n g e n e r f o lg t d u r c h e n e r g e t is c h e B e t r a c h t u n g e n ; d ie s e k u n d lic h e E n e r g ie m e n g e , w e lc h e d u r c h d ie F lä c h e n e in h e i t h i n d u r c h t r it t , a ls o d ie S c h a llin t e n s it ä t , m u ß n o t w e n d ig e r w e is e iib e re in - s tim m e n m it d e m B e t r a g a n S c h w in g u n g s e n e r g ie , w e lc h e r in e in e m Z y lin d e r e n t h a lt e n is t, d e sse n G r u n d flä c h e d ie e r w ä h n t e F lä c h e n e in h e it is t u n d d e sse n H ö h e g le ic h d e r S t r e c k e is t, w e lc h e d ie W e lle in e in e r S e k u n d e d u r c h lä u f t. P o t e n t ie lle u n d k in e tis c h e E n e r g ie sin d (w en n g e n ü g e n d W e lle n lä n g e n im Z y lin d e r e n t h a lt e n sind) e in a n d e r p r a k t is c h g le ic h , m a n k a n n a lso , a n s t a t t s ic h d e n Z y lin d e r h a lb m it p o t e n t ie lle r u n d h a lb m it k in e t is c h e r E n e r g ie a n g e f ü llt zu d e n k e n , ih n e n t w e d e r a ls v o lls t ä n d ig m it p o t e n t ie lle r E n e r g ie o d e r v o lls t ä n d ig m it k in e t is c h e r E n e r g ie a n g e f ü llt a u ffa s s e n . D ie B e z ie h u n g e n 3 b z w . 4 sin d a u f G ru n d d ie s e r A n n a h m e le ic h t zu v e r ifiz ie r e n .
K o m b in ie r t m a n G le ic h u n g (4) u n d (3), so e r h ä lt m a n d a s w ic h t ig e R e s u lt a t (5), d a ß in d e r e b e n e n W e lle D r u c k u n d G e s c h w in d ig k e it e in a n d e r p r o p o r tio n a l sin d , d e r P r o p o r t io n a lit ä t s fa k t o r is t e in e K o n s t a n t e , u n d in s b e s o n d e re v o m O r t d e r B e o b a c h t u n g u n a b h ä n g ig .
W ir w e rd e n a u f d ie se s R e s u lt a t n o c h zu sp re ch e n k o m m e n b e i B e s p r e c h u n g d e r M e ß m e th o d e n , m it d e re n H ilfe m a n d ie g e n a n n te n G r ö ß e n e r m it t e ln k a n n . D ie B e z ie h u n g e n 2— 5 z e ig e n , d a ß z u I n t e n s it ä ts b e s tim m u n g e n in e b e n e n , f o r t la u fe n d e n W e lle n so w o h l M e s su n g e n d e r D r u c k a m p lit u d e [z. B . m it t e ls e in e s K o n d e n s a t o r m ik r o p h o n s ) w ie
25
2g8 T r e n d e l e n b ü r g : Ü b er S ch allfeld p ro blem e. T Die Natur- Lwissenschaften a u c h M e s su n g e n d e r G e s c h w in d ig k e it s a m p lit u d e
(z. B . m it t e ls d e r R a y le ig h - S c h e ib e ) o h n e w e ite r e s v e r w e n d e t w e r d e n k ö n n e n . D ie U m r e c h n u n g s f a k t o r e n b e s itz e n d ie f ü r d a s g a n z e S c h a llfe ld k o n s ta n t e n W e r t e — -— (4) b z w . —— — (3).
2 o • u 2
K o m p liz ie r t w e r d e n d ie V e r h ä lt n is s e d a n n , w e n n k e in e e b e n e n W e lle n v o r lie g e n . E s is t d a n n n ic h t m e h r m ö g lic h , d ie Z u s a m m e n h ä n g e z w is c h e n E l o n g a tio n , G e s c h w in d ig k e it , D r u c k u n d I n t e n s i t ä t d u r c h so e in fa c h e e n e r g e t is c h e B e t r a c h t u n g e n a b z u le it e n , w ie w ir es f ü r d ie e b e n e W e lle d u r c h fü h r e n k o n n te n . I n s o lc h e n F ä ll e n fü h r e n w ir v o r t e i l h a f t d a s G e s c h w in d ig k e it s p o t e n t ia l a ls e in e w e ite r e a k u s t is c h e G r ö ß e e in . D a s G e s c h w in d ig k e it s p o t e n t i a l is t so d e fin ie r t , d a ß d ie D iff e r e n t a t io n d ie s e r F u n k t i o n n a c h d e r R a u m k o o r d in a t e d ie G e s c h w in d ig k e it s k o o r d in a t e e r g ib t u n d d a ß d ie z e it lic h e A b le it u n g d e s G e s c h w in d ig k e it s p o t e n t ia ls p r o p o r t io n a l zu d e m D r u c k a n d e r b e t r e ffe n d e n S te lle is t .
<50 , 6<P
p = _ e _ ( 6 ) „ = _ _ (7)
W ir w o lle n m it L o r d R a y l e i g h d a s S c h a U fe ld e in e r k u g e lfö r m ig e n S c h a llq u e lle b e t r a c h t e n , d ie K u g e lo b e r flä c h e f ü h r t e a n a lle n P u n k t e n p h a s e n g le ic h e B e w e g u n g e n g le ic h e r A m p lit u d e a u s . ( A t m e n d e K u g e l.) E s w ir d d a n n d a s G e s c h w in d ig k e i t s p o t e n t i a l
,I,=- ^ 7 c o s H ! - ^ } ) ( 8 )
w o b e i Q d ie A m p lit u d e d e s M e d iu m s t i'o m e s 1) b e d e u t e t .
D ie g e n a u e D u r c h fü h r u n g d e r R e c h n u n g , w ie sie d u r c h H a h n e m a n n u n d H e c h t 2) e r f o lg t e , e r g i b t d ie fo lg e n d e n B e z ie h u n g e n :
g coQ . \ ( r \1 4 n r
v = --- 1 1coQ
4 71 T U ]/ l + V
(9)
</j (IO)
(II)
D ie z e it lic h e P h a s e k ö n n e n w ir a u ß e r a c h t la ss e n , sie is t a k u s t is c h u n w e s e n tlic h . S e h r w ic h t ig is t a b e r d ie F e s t s t e llu n g , d a ß d e r P r o p o r t i o n a li t ä t s f a k t o r v o n D r u c k u n d G e s c h w in d ig k e it n u n n ic h t m e h r e in e n k o n s t a n t e n u n d in s b e s o n d e r e v o m O r t u n a b h ä n g ig e n W e r t b e s i t z t : b e i d e r K u g e lw e lle t r i t t h ie r g e g e n ü b e r d e r e b e n e n W e lle e in K o r r e k t u r f a k t o r e in .
F ü r d ie I n t e n s i t ä t g e lt e n d ie B e z ie h u n g e n
j = + y ^ ) ' } (.2)
j 2 Q • UV
x) W . H a h n e m a n n u n d H . H e c h t , P h y s. Z eitsch r.
18, 261. 19 17 .
2) W . H a h n e m a n n und H . H e c h t , P h y s. Z eitsch r.
17, 601. 1916.
E s z e ig t in s b e s o n d e r e n o c h d ie B e z ie h u n g 12, d a ß e in e G e s c h w in d ig k e its m e s s u n g im S c h a llfe ld , n ic h t m e h r , w ie b e i e b e n e n W e lle n , o h n e w e ite r e s z u r I n t e n s i t ä t s m e s s u n g b e n u t z t w e r d e n k a n n , es i s t im G e g e n te il e r fo r d e r lic h , a u c h h ie r b e i d e n v o m O r t a b h ä n g ig e n F a k t o r 1 + ( — — Y z u b e r ü c k s ic h t ig e n . D e r E i n s a t z e in e s D r u c k e m p f ä n g e r s g e s t a t t e t es je d o c h a u c h h ie r , o h n e w e ite r e s d ie I n t e n s i t ä t z u b e s tim m e n ( v g l. 13).
N o c h s c h w ie r ig e r w e r d e n d ie V e r h ä lt n is s e in k o m p liz ie r t e r e n S c h a llfe d e r n . V o n H . B a c k h a u s 1) w u r d e n d ie V e r h ä lt n is s e u n t e r s u c h t , w ie sie im S c h a llfe ld e in e r in e in e r s t a r r e n WTa n d s c h w in g e n d e n K o lb e n m e m b r a n v o r lie g e n . D ie U n te r s u c h u n g e n sin d n o c h n ic h t a b g e s c h lo s s e n , e in ig e E r g e b n is s e s o lle n a b e r b e r e it s h ie r b e s p r o c h e n w e r d e n , w e il sie in t e r e s s a n t e E in b lic k e in d ie S c h a llf e l d k o n f ig u r a t io n e in e s d e r a r t ig e n S t r a h le r s g e w ä h r e n .
L o r d R a y l e i g h h a t d e n a llg e m e in e n A n s a t z d ie s e s P r o b le m s g e g e b e n . E r fin d e t , d a ß d a s G e s c h w in d ig k e it s p o t e n t ia l <I> im S c h a llfe ld e in e r K o lb e n m e m b r a n , d ie in e in e r u n e n d lic h a u s g e d e h n t e n s t a r r e n W a n d s c h w in g t , fo lg e n d e r m a ß e n d a r s t e llb a r i s t :
1 r r ö <I> e ~ ikr , „
0 = — —— / l- z --- d)S . (14) 2 Jtj j ön r
H ie r b e i is t d S d a s F lä c h e n e le m e n t d e r M e m b r a n , d ie I n t e g r a t io n is t zu e r s tr e c k e n ü b e r d ie s e F lä c h e , r is t d ie E n t fe r n u n g d e s A u f p u n k t e s v o n d e m b e tr e ffe n d e n F lä c h e n e le m e n t k , w o b e i X d ie W e lle n lä n g e b e d e u te t, n is t d ie R ic h t u n g d e r F lä c h e n n o r m a le n d e r M e m b r a n .
D ie I n t e g r a t io n is t e le m e n ta r d u r c h f ü h r b a r fü r d ie je n ig e n A u f p u n k t e , d ie a u f d e r M itte ls e n k r e c h t e n d e r a ls k r e is fö r m ig a n g e n o m m e n e n K o lb e n m e m b r a n lie g e n . E s e r g ib t s ic h f ü r d a s G e s c h w in d ig k e it s p o t e n t ia l a u f d e r M it t e la c h s e :
<l> = - x sin{ 2 (m + & - z0)} • | ^
\ < o t - ~ ( ^ z i + w + z 0)\
5)
w o b e i Z0 d ie E n t fe r n u n g d e s A u f p u n k t e s v o n d e r M e m b r a n u n d v d ie G e s c h w in d ig k e it in d e r M e m b r a n e b e n e b e d e u te t. R is t d e r M e m b r a n r a d iu s . D ie D is k u s s io n d ie s e r B e z ie h u n g e r g ib t ein in te r e s s a n te s R e s u lt a t : D ie v o n e in e r e b e n e n K o l b e n m e m b r a n a b g e s t r a h lt e a k u s tis c h e W e lle b e s i t z t e in e A m p lit u d e , d ie v o m O r t in e in e r v e r w ic k e lte n B e z ie h u n g a b h ä n g t, u n d z w a r l ä ß t sich d ie A m p lit u d e s c h r e ib e n :
(16)
(13) D ie A m p lit u d e ä n d e r t s ic h a ls o r ä u m lic h z w is c h e n 0 u n d . A n d e n S te lle n , w o + B2 — Z u)
*) H . Ba c k h a u sund F . Tr e n d e l e n b u r g, Z eitsch r.
f. techn. P h ys. V I I , 630. 1926.
— n ji is t, w o b e i n e in e b e lie b ig e g a n z e p o s itiv e Z a h l b e d e u te t, fin d e t v ö llig e A u s lö s c h u n g s t a t t . 1 )ie A u s lö s c h u n g s p u n k t e sin d d a r s t e llb a r d u r c h d ie B e z ie h u n g
^ R 2 2
^0 - - j j r ~ n2
--- (1 7 )
2 n v u
~ JT
S o lc h e P u n k t e v o lls t ä n d ig e r A u s lö s c h u n g k ö n n e n a lso n u r in e n d lic h e r A n z a h l v o r h a n d e n se in , so la n g e
Heit 13. I 1. 4. 1927 |
D ie B e d in g u n g e n f ü r d a s E n t s t e h e n s o lc h e r I n t e r fe re n z e n sin d a ls o u m so g ü n s tig e r , je g r ö ß e r d a s V e r h ä lt n is M e m b r a n r a d iu s z u r W e lle n lä n g e is t.
A u s d r u c k 15 z e ig t, d a ß d ie B e z ie h u n g z w is c h e n D r u c k u n d G e s c h w in d ig k e it a u ß e r o r d e n t lic h k o m p liz ie r t is t, d e r D r u c k is t e in fa c h p r o p o r tio n a l se lb st, w ä h r e n d in d e r G e s c h w in d ig k e it s a m p lit u d e e in k o m p liz ie r t e r A u s d r u c k , w e lc h e r v o n d e r rä u m lic h e n K o o r d in a t e a b h ä n g t , e in g e h t.
S e t z t m a n a ls o in d e r a r t ig e S c h a llfe ld e r v e r s c h ie d e n e E m p fä n g e r e in , v o n d e n e n e in T e il a u f D r u c k s c h w a n k u n g u n d e in T e il a u f G e s c h w in d ig k e it s a m p lit u d e a n s p r ic h t, so k a n n m a n im a l l g e m e in e n k e in e ü b e r e in s tim m e n d e n R e s u lt a t e e r w a rte n . W ir w e r d e n h ie r a u f n o c h b e i D is k u s s io n d e r M e s su n g e n , d ie in S c h a llfe ld e r n d u r c h g e f ü h r t w u rd e n , z u r ü c k k o m m e n .
A u ß e r h a lb d e r M it t e ln o r m a le n is t d ie D u r c h r e c h n u n g d e s G e s c h w in d ig k e it s p o t e n tia le s m it e in fa c h e n M it t e ln n ic h t d u r c h fü h r b a r . G e w is s e
\ o r a u s s a g e n la s s e n s ic h a b e r a n H a n d a n a lo g e r o p t is c h e r E r s c h e in u n g e n (F R A U N H O F E R S ch e B e u g u n g sb ild e r ) m a c h e n . H ie r a u f w e r d e n w ir b e i D is k u ss io n d e r M e ß e r g e b n is s e z u r ü c k k o m m e n .
D ie b is h e r ig e n Ü b e r le g u n g e n b e z o g e n sich le d ig lic h a u f e in fa c h h a r m o n is c h e V o r g ä n g e . H a n d e lt es s ic h u m z u s a m m e n g e s e tz t e K lä n g e , so g e lte n d ie e n ts p r e c h e n d e n B e z ie h u n g e n f ü r je d e n e in z e ln e n T e ilt o n . D a je d e r a k u s tis c h e V o r g a n g — w e n n m a n n u r d ie G r u n d p e r io d e g e g e b e n e n fa lls e n t s p r e c h e n d la n g w ä h lt — d u r c h e in e F o u r ie r re ih e d a r g e s t e llt w e r d e n k a n n , s in d d ie in d e n v o r s te h e n d e n A u s fü h r u n g e n b e s p r o c h e n e n a k u s t is c h e n G r u n d b e z ie h u n g e n g a n z a llg e m e in v e r w e n d b a r ; in e in ig e n F ä ll e n k ö n n e n E r g ä n z u n g e n v o n V o r t e il sein . A ls e in B e is p ie l h ie r fü r se ie n d ie je n ig e n a k u s tis c h e n V o r g ä n g e , d ie m a n m it d e m N a m e n K n a l l b e z e ic h n e t , g e n a n n t. E in K n a l l k a n n v o r t e ilh a f t d u r c h z w e i p h y s ik a lis c h e G r ö ß e n g e k e n n z e ic h n e t w e r d e n : d ie m it t le r e I n t e n s i t ä t u n d d ie g e s a m te w ä h r e n d d e s K n a l le s d u r c h e in e n b e s t im m te n Q u e r s c h n it t h i n d u r c h g e t r e t e n e E n e r g ie m e n g e . D ie A b le it u n g d ie s e r G r ö ß e n is t o h n e w e ite r e s m ö g lic h , w e n n m a n (b e is p ie ls w e is e d u r c h A u f z e ic h n e n d e r D r u c k a m p lit u d e d e s K n a llv o r g a n g e s ) d ie M o m e n t a n in t e n s it ä t b e s t im m t , a u s d ie s e r f o lg t d u rc h M it t e lw e r t s b ild u n g d ie m it t le r e I n t e n s i t ä t u n d d u r c h I n t e g r a t io n ü b e r d ie Z e it d ie G e s a m t e n e rg ie d e s K n a l l V o rg a n g e s.
W ir h a b e n u n s b is la n g n u r m it d e r p h y s ik a lis c h e n I n t e n s i t ä t e in e s a k u s t is c h e n V o r g a n g s b e s c h ä f t ig t . D e r Z u s a m m e n h a n g z w is c h e n p h y s i k a lis c h e r I n t e n s i t ä t u n d S t ä r k e d e r G e h ö r e m p fin d u n g ( s u b je k t iv e r L a u ts t ä r k e ) is t v e r w ic k e lt . E i n m a l h ä n g t d ie L a u t s t ä r k e v o n d e r F r e q u e n z d e r e rre g e n d e n S c h w in g u n g a b , z u m a n d e r e n is t sie v o n d e r A m p lit u d e n ic h t n a c h e in e m lin e a re n G e s e t z a b h ä n g ig , u n d s c h lie ß lic h is t in d e n je n ig e n F ä lle n , in d e n e n m e h r e re T e ilt ö n e a u f d a s O h r t r e ffe n , d ie s u b je k t iv e L a u t s t ä r k e n ic h t e in fa c h g le ic h d e r S u m m e d e r je n ig e n L a u t s t ä r k e n , w e lc h e je d e r e in z e ln e T e ilt o n fü r s ic h h e r v o r r u fe n w ü rd e . M essen w ir a ls o d ie I n t e n s i t ä t m it p h y s ik a lis c h e n M itte ln , so m ü ss e n w ir fü r d ie U m r e c h n u n g a u f s u b je k t iv e L a u t s t ä r k e d ie s k iz z ie r t e n V e r h ä lt n is s e b e r ü c k s ic h tig e n . D ie in F r a g e s t e h e n d e n B e z ie h u n g e n sin d d u r c h d ie A r b e it e n a m e r ik a n is c h e r F o r s c h e r (u n te r d e n e n b e s o n d e r s Kn u d s e n, s o w ie We g e l u n d La n e1) z u n e n n e n sind ) im w e s e n tlic h e n g e k lä r t . F ü r p r a k t is c h e Z w e c k e k a n n es n a t ü r lic h v o r t e i lh a f t sein , d ie o b je k t iv e n M e s su n g e n , w e lc h e d ie B e r ü c k s ic h t ig u n g d ie s e r B e z ie h u n g e n e r fo rd e r n , zu u m g e h e n u n d sic h s t a t t d e s se n m it L a u t s t ä r k e m e s s u n g e n d u r c h s u b je k t iv e n V e r g le ic h zu b e- b e g n ü g e n ; e in e v o r t e ilh a f t e A n o r d n u n g h ie r z u s c h u f Ma c Ke n z i e2) n a c h A r t d e s F li c k e r - P h o t o m e te r s : D e m O h r w ir d in z e it lic h s c h n e lle r F o lg e a b w e c h s e ln d d e r zu u n t e r s u c h e n d e K l a n g u n d e in b e k a n n te r V e r g le ic h s k la n g z u g e fü h r t . D a s V e r s c h w in d e n d e r T r ille r e m p f in d u n g d e u t e t a u f g le ic h e s u b j e k t i v e L a u t s t ä r k e . H . B a r k h a u s e n 3) h a t a ls e in fa c h e s u b je k t iv e M e th o d e a ls V e r g le ic h s s c h a ll
q u e lle e in e n e le k t r is c h e r r e g t e n S u m m e r v o r g e s c h la g e n . D a s S u m m e r g e r ä u s c h b e s it z t e in a u s g e d e h n te s F r e q u e n z s p e k t r u m , so d a ß V e r g le ic h s m e s s u n g e n m it G e r ä u s c h e n a n d e r e r N a t u r e in e n g u t e n A n h a lt ü b e r d ie s u b je k t iv e L a u t s t ä r k e g e b e n k ö n n e n .
D ie g r u n d le g e n d e n B e t r a c h t u n g e n ü b e r d ie a k u s t is c h e n G rö ß e n k ö n n e n w ir j e t z t v e r la s se n u n d u n s d e n M e th o d e n zu q u a n t it a t iv e n S c h a llf e l d m e ss u n g e n z u w e n d e n . D ie M e th o d e n z u r A u s m e ss u n g v o n S c h a llfe ld e r n h a b e n n u r d a n n A u s s i c h t a u f q u a n t i t a t i v b r a u c h b a r e R e s u lt a t e , w e n n d u r c h d ie in d a s S c h a llfe ld e in g e s e tz te n A n o r d n u n g e n k e in e r le i S c h a llfe ld v e r z e r r u n g e n v o r g e n o m m e n w e rd e n . U r s a c h e zu V e r z e r r u n g e n k ö n n e n z w e i E r s c h e in u n g e n b i e t e n : I s t d ie r ä u m lic h e A u s d e h n u n g d e s E m p fä n g e r s g r o ß g e g e n d ie W e lle n lä n g e e in e r im S c h a llfe ld v o r h a n d e n e n S c h w in g u n g , so w ir d d ie s e W e lle r e f le k t ie r t , b e s i t z t d e r E m p fä n g e r e in e s c h w a c h g e d ä m p ft e R e s o n a n z s te lle , so w ir k t e r fü r d ie b e t r e ffe n d e F r e q u e n z a ls S c h a ll
a n t e n n e u n d s t ö r t d a s S c h a llfe ld d u r c h A b s o r p tio n . In b e z u g a u f d ie se S t ö r u n g s m ö g lic h k e it m ü sse n
*) R . L . W e g e l , B ell. sy st, techn . jou rn . I, 57.
1922; O. Kn u d s e n, P h y s. R e v . 2 1 , 84. 1923; R . L . W e g e l und. L a n e , P h ys. R e v . 23 , 266. 1924.
2) D. M a c K e n z i e , P h y s. R e v . 20, 331. 1922.
3) H . Ba r k h a u s e n, Zeitschr. f. techn. P h vs. V I I, 599. 1926.
T r e n d e l e n b u r g : Ü b e r S ch allfeld p ro b lem e. 299
2 5 *
30 0 T r e n d e l e n b u r g : Ü ber S ch allfeld p ro b lem e. f Die Natur- I Wissenschaften a lle S c h a lle m p fä n g e r k r it is c h g e w e r t e t w e rd e n ,
w e lc h e in A n o r d n u n g e n z u M e s s u n g v o n S c h a ll
fe ld e r n e in g e s e tz t w e r d e n .
U n t e r d e n M e t h o d e n z u r S c h a llfe ld m e s s u n g is t e in e d e r ä lt e s t e n d ie je n ig e d e r R A Y L E iG H sclien S c h e ib e . D ie s e a n s ic h z ie m lic h u n e m p fin d lic h e M e th o d e h a t in d e r n e u e s te n Z e it , w o es s ic h v ie lf a c h u m M e s s u n g e n in S c h a llfe ld e r n g r o ß e r I n t e n s i t ä t , z. B . in S c h a llf e ld e r n v o n L a u t s p r e c h e r n h a n d e lt, w ie d e r a n B e d e u t u n g g e w o n n e n ; d e r g r ö ß t e V o r t e i l d e r R A Y L E iG H sch e n S c h e ib e is t es, d a ß d ie v o r g e n o m m e n e n A b le s u n g e n s ic h u n s c h w e r a u f a b s o lu t e W e r t e u m r e c h n e n la s s e n 1). D ie R a y - LEiGH Sche S c h e ib e is t a n e in e m d ü n n e n Q u a r z fa d e n a u f g e h ä n g t , in d e r W e is e , d a ß sie im R u h e z u s t a n d u n t e r 45 0 z u r F o r t p f la n z u n g s r ic h t u n g d e r S c h a llw e lle n s t e h t . D ie v o r b e iz ie h e n d e S c h a l l w e lle ü b t a u f d ie S c h e ib e e in D r e h m o m e n t M a u s , w e lc h e s s ic h n a c h d e n B e r e c h n u n g e n Kö n i g s a n g e b e n l ä ß t zu
M — k • v ' 2
w o b e i k e in e A p p a r a t k o n s t a n t e is t, d ie in s b e s o n d e r e v o m R a d iu s d e r S c h e ib e a b h ä n g t . D ie Ra y l e i g h- s c h e S c h e ib e is t a ls o e in G e s c h w in d ig k e it s e m p fä n g e r u n d z w a r i s t ih r A u s s c h la g p r o p o r t io n a l d e m Q u a d r a t d e r G e s c h w in d ig k e it .
D a s D r e h m o m e n t is t d u r c h d ie m it m e c h a n is c h e n M it t e ln b e s t im m b a r e T o r s io n s k r a ft d e s F a d e n s u n d d e n A b le n k u n g s w in k e l d e f in ie r t , d ie G e s c h w in d ig k e it s a m p lit u d e d e r S c h a llt e ilc h e n k a n n s o m it in a b s o lu te m M a ß e b e s t im m t w e rd e n .
D ie B e z ie h u n g e n z w is c h e n G e s c h w in d ig k e it s a m p lit u d e , D r u c k a m p lit u d e , T e ilc h e n a m p lit u d e u n d I n t e n s i t ä t h a t t e n w ir o b e n b e s p r o c h e n , d ie s e a k u s t is c h e n G r ö ß e n k ö n n e n s o m it a u s d e n M e s su ngen m it d e r RAY L EiG H schen S c h e ib e e r m it t e lt w e rd e n .
D ie RAYLEiGH Sche S c h e ib e e r f ü llt a lle B e d in g u n g e n , w e lc h e m a n v o m S t a n d p u n k t d e r V e r m e id u n g v o n S c h a llf e ld s t ö r u n g e n s t e lle n m u ß . d a n n , w e n n ih r e A u s d e h n u n g k le in g e g e n d ie W e lle n lä n g e d e r h ö c h s te n im S c h a llfe ld n o c h v o r h a n d e n e n F r e q u e n z g e h a lt e n w ir d . D ie s e F o r d e r u n g is t b is zu F r e q u e n z e n v o n e t w a 10 000 H e r t z e r fü llb a r .
E s is t n a c h d e m G e s a g te n m ö g lic h , e in S c h a ll
fe ld m it d e r R A Y L E iG H -Scheib e a u s z u m e s s e n u n d z. B . d ie G e s a m t le is t u n g e in e r S c h a llq u e lle a n z u g e b e n , in d e m m a n d ie I n t e n s i t ä t a u f e in e r g e schlossenen, u m d ie S c h a llq u e lle g e le g te n F lä c h e b e s t im m t u n d d ie g e m e s s e n e n W e r t e ü b e r d ie F lä c h e in t e g r ie r t . P r a k t is c h is t es je d o c h u n m ö g lic h , d ie R A Y L E iG H -Scheib e h ie r z u e in z u s e t z e n , d a sie e in e s e h r s o r g fä lt ig e u n d in s b e s o n d e r e o r t s fe s te A u f h ä n g u n g e r fo r d e r t u n d g e g e n ä u ß e r e S t ö r u n g e n , w ie L u f t z u g , se h r e m p fin d lic h is t. S o w ir d m a n z u d ie s e m Z w e c k v o r t e i l h a f t e in e a n d e r e
x) V g l. hierzu insbesondere: W . K o e n i g , W ied e
m anns A n n. 43, 43. 18 9 1; W . Z e r n o v , A nn. d. P h y s. 26, 79. 1908; E . M e y e r , E .N .T . 290. 1926; Z e itsch r. f.
tech n . P h y s. V I I , 609. 1926.
G r u p p e v o n S c h a lle m p fä n g e r n w ä h le n , w e lc h e e b e n fa lls q u a n t i t a t i v b r a u c h b a r e R e s u lt a t e e r g e b e n , e s s in d d ie s d ie e le k t r is c h e n S c h a lle m p fä n g e r . M a n k a n n d ie zu S c h a llfe ld m e s s u n g e n b e n u t z t e n e le k t r is c h e n E m p fä n g e r n a c h z w e i G e s ic h ts p u n k t e n e in t e ile n : 1. E m p fä n g e r zu M e s s u n g e n a n e in f a c h h a r m o n is c h e n V o r g ä n g e n , 2. M e t h o d e n z u r o b je k t iv e n A u f z e ic h n u n g v o n S c h a llf e ld V o rg ä n g e n .
D ie u n t e r 2. fa lle n d e n M e t h o d e n g e s t a t t e n a lle d ie je n ig e n M e s su n g e n , w e lc h e m it d e n u n t e r 1. a u f z u z ä h le n d e n M e t h o d e n a u s fü h r b a r s in d . T r o t z d e m s o lle n d ie M e t h o d e n u n t e r 1. g e s o n d e r t b e h a n d e lt w e r d e n , d a sie z w a r n ic h t so a llg e m e in v e r w e n d b a r sin d , d a fü r a b e r in b e s o n d e r e n F ä ll e n , w o es s ic h u m d ie U n t e r s u c h u n g v o n r e in h a r m o n is c h e n V o r g ä n g e n h a n d e lt , V o r t e ile in H i n s i c h t d e r B e q u e m lic h k e it u n d d e r G e n a u ig k e it b ie t e n .
M e s s u n g e n a n e in f a c h h a r m o n is c h e n V o r g ä n g e n g e s t a t t e t d ie S c h a lld r u c k k o m p e n s a t io n s m e th o d e n a c h E . Ge r l a c h1 ). D e r S c h a ll t r i f f t a u f e in e n n a c h d e m P r in z ip d e s B ä n d c h e n m ik r o p h o n s a r b e it e n d e n E m p fä n g e r . D u r c h d a s B ä n d c h e n w ir d e in S tr o m g e le it e t , w e lc h e r d ie s e lb e F r e q u e n z w ie d e r z u m e s s e n d e S c h a llv o r g a n g b e s i t z t u n d d e s se n S tr o m , A m p lit u d e u n d P h a s e , so g e w ä h lt w ir d , d a ß d ie e le k t r o d y n a m is c h e n K r ä f t e d e s S tr o m e s d ie v o n d e m S c h a lld r u c k a u f d a s B ä n d c h e n h e r r ü h r e n d e n a k u s t is c h e n K r ä f t e k o m p e n sie r e n , so d a ß d a s B ä n d c h e n in R u h e b le i b t u n d k e in e r le i B e w e g u n g a u s fü h r e n k a n n . D ie g e n a u e A b g le ic h u n g d e r e le k t r o d y n a m is c h e n K r ä f t e g e g e n d ie a k u s t is c h e n K r ä f t e f o l g t d a d u r c h , d a ß m a n h in t e r d e m B ä n d c h e n m it e in e m H ö r s c h la u c h a b h ö r t o d e r a b e r d a d u r c h , d a ß m a n m it e in e r e le k tr is c h e n B r ü c k e n s c h a l t u n g u n d V e r s t ä r k e r a r b e it e t u n d a u f re in e le k t r is c h e m W e g e d ie K o m p e n s a t io n e in s te llt. D a s g e s c h ild e r te V e r f a h r e n b e s i t z t h i n s ic h t lic h d e r A b h ä n g ig k e it v o n d e r A m p l i t u d e u n d v o n d e r P h a s e in fo lg e d e r K o m p e n s a t io n a u f N u ll e in e b e t r ä c h t lic h e G e n a u ig k e it .
E . Me y e r2) b e n u t z t z u r S c h a lld r u c k k o m p e n s a tio n e in e le k t r o s ta tis c h e s V e r f a h r e n . D ie M e m b r a n e in e s K o n d e n s a t o r m ik r o p h o n s w ir d d u r c h e le k t r o s t a t is c h e K r ä f t e , d ie d e m S c h a lld r u c k e n t g e g e n g e s e t z t g le ic h sin d , k o m p e n s ie r t, d ie E i n s t e llu n g a u f N u ll e r f o lg t u n t e r Z u h ilfe n a h m e e in e r H o c h fr e q u e n z s c h a lt u n g , w e lc h e d ie K a p a z i t ä t s ä n d e r u n g e n d e s K o n d e n s a t o r m ik r o p h o n s in e m p fin d lic h e r W e is e zu b e o b a c h t e n g e s t a t t e t . D ie A n o r d n u n g n a c h E . Me y e r z e ic h n e t s ic h d a d u r c h a u s , d a ß sie e in e n S c h a lle m p f ä n g e r v e r w e n d e t , d e s se n r ä u m lic h e A u s d e h n u n g se h r g e r in g is t, d a s S c h a llfe ld w ir d p r a k t is c h n ic h t b e e in f lu ß t .
D ie K o m p e n s a t io n s m e t h o d e n sin d f ü r e in fa c h e h a r m o n is c h e V o r g ä n g e o h n e w e ite r e s zu b e n u t z e n , a u c h d ie U n t e r s u c h u n g z u s a m m e n g e s e t z t e r K lä n g e i s t m ö g lic h , in d e m m a n z e itlic h n a c h e in a n d e r fü r
x) E . G e r l a c h , W iss. V e rö ffe n tl. a. d. Siem ens- K o n zern 3, 139. 1923.
2) E . M e y e r , Zeitsch r. f. techn . P h ys. V I I , 609.
1926.
Heft 13. 1
1. 4. 1927 J T r e n d e l e n b u r g : Ü b er Sch allfeldp roblem e. 3 0 1
d ie e in z e ln e n le i l k l ä n g e d ie K o m p e n s a t io n d u r c h fü h r t. D ie M e th o d e n v e r s a g e n je d o c h n o t w e n d ig e r w e ise fü r z e itlic h b e g r e n z t e o d e r z e it lic h sc h n e ll v e r ä n d e r lic h e S c h a llv o r g ä n g e , w ie d ie s b e is p ie ls w e ise v ie le S p r a c h - u n d M u s ik k lä n g e d a r s te lle n . H ie r is t es e rfo rd e r lic h , z u n ä c h s t d ie K lä n g e a u f z u z e ic h n e n u n d d a n n d ie r e g is tr ie r te n K la n g b ild e r m e ß te c h n is c h a u s z u w e r t e n .
D ie V e r fa h r e n z u r e le k t r is c h e n K la n g a u fz e ic h n u n g b e d ie n e n s ic h d e s K o n d e n s a t o r m ik r o p h o n s a ls S c h a lle m p fä n g e r , u n d z w a r w u r d e in D e u t s c h la n d d a s K o n d e n s a t o r m ik r o p h o n v o n H . Ri e g g e r1) u n d in A m e r ik a d a s K o n d e n s a t o r m ik r o p h o n v o n E . C. We n t e2) e in g e s e tz t. B e id e E m p fä n g e r sin d in ih re n a k u s tis c h e n u n d e le k t r is c h e n E ig e n s c h a fte n so d e fin ie r t , d a ß d ie g e w o n n e n e n R e s u l
t a t e q u a n t i t a t i v b r a u c h b a r s in d ; in sb e s o n d e re is t
E ic h u n g e n m it d e m T h e r m o p h o n a ls S c h a ll
q u e lle b e s itz e n e in e n p r in z ip ie lle n N a c h t e il: die M a x im a lle is tu n g , w e lc h e m a n d e m T h e rm o p h o n e n tn e h m e n k a n n , is t so g e r in g , d a ß e in e E ic h u n g im fre ie n S c h a llfe ld u n m ö g lic h is t. T h e rm o p h o n u n d E m p fä n g e r m ü ss e n in e in e m e n g e n , a lls e its m it s ta r re n W ä n d e n u m g e b e n e n H o h lr a u m e in g e sc h lo s se n w e rd e n , e in so lc h e s V o r g e h e n b e w ir k t a b e r, d a ß d ie E in s e t z u n g s b e d in g u n g e n d e s S c h a ll
e m p fä n g e r s a n d e r e sin d a ls im fre ie n S c h a llfe ld . E s w ir d a u f d ie s e W e is e u n t e r a n d e r e m d ie S t r a h lu n g s d ä m p fu n g d e s E m p fä n g e r s v e r ä n d e r t .
F ü r d ie E ic h u n g d e s f ü r u n s e re M e s su n g e n b e n u t z t e n R iE G G E R sch en H o c h fr e q u e n z k o n d e n s a t o r m ik r o p h o n s w u r d e a u s d ie s e n G r ü n d e n e in e a n d e re A n o r d n u n g g e w ä h lt 1) :
A ls S c h a llq u e lle z u r E r r e g u n g d e s S c h a llfe ld e s
m ikrophons.
F ig. 1. D ie E ich an ord n un g.
zu e rw ä h n e n , d a ß d ie g e n a n n te n E m p fä n g e r g e e ic h t w u rd e n . E s sei j e t z t k u r z s k iz z ie r t , w ie d ie se E ic h u n g e n d u r c h g e fü h r t w u r d e n . D e r A n s c h lu ß d es a m e r ik a n is c h e n E m p fä n g e r s a n d a s C G S - S y s t e m e r fo lg t e d u r c h E ic h u n g in e in e m S c h a ll
v o r g a n g b e s t im m t e r D r u c k a m p lit u d e . A ls S c h a ll
q u e lle d ie n te d a s T h e r m o p h o n : I n e in e m w e c h s e l
s t r o m d u r c h flo s s e n e n d ü n n e n S t r o m le it e r e n t s te h e n T e m p e r a t u r s c h w a n k u n g e n in d e r P e r io d e d e r W e c h s e lle is t u n g ; d ie s e T e m p e r a t u r s c h w a n k u n g e n d r in g e n in d a s u m g e b e n d e M e d iu m a ls r ä u m lic h g e d ä m p fte T e m p e r a tu r w e lle n e in u n d b e w ir k e n d o r t D r u c k s c h w a n k u n g e n , d ie s ic h a ls S c h a ll
w e lle n a u s b r e ite n . D ie A m p lit u d e d e r D r u c k s c h w a n k u n g e n k a n n a u f G ru n d d e r e le k t r is c h e n u n d th e r m is c h e n E ig e n s c h a ft e n d e s T h e r m o p h o n s b e r e c h n e t w e r d e n , so d a ß e in e E m p fä n g e r e ic h u n g a u c h in a b s o lu t e m M a ß e m ö g lic h is t.
H . R i e g g e r , W iss. V erö ffen tl. a. d. Siem ens- K onzern 3, 67. 1924; F . T r e n d e l e n b u r g , W iss. V e r öffen tl. a. d. S iem en s-K on zern 3, 43- i 9 24 -
2) E . C. W e n t e , P h y s. R e v . 10, 39. 1917-
d ie n te d e r B la t t h a lle r . D ie I n t e n s i t ä t r e c h n e r is c h a u s d e n e le k t r is c h e n D a t e n z u e r m it te ln , w ä r e n u r s c h w e r m ö g lic h , d a d e r B la t t h a lle r e in e S c h a ll
q u e lle v o n b e tr ä c h t lic h e r r ä u m lic h e r A u s d e h n u n g d a r s t e llt u n d a u s d ie s e m G ru n d e , w o r a u f w ir n o c h z u sp r e c h e n k o m m e n , e in S c h a llfe ld k o m p liz ie r t e r K o n f ig u r a t io n e rre g t. D ie S c h a llin t e n s it ä t w u r d e d a h e r e x p e r im e n te ll b e s tim m t, z u r M e s su n g d ie n te d ie RAYLEiGH sche S c h e ib e . K o n d e n s a t o r m ik r o p h o n u n d R AYLEiGH sche S c h e ib e w u r d e n ö r t lic h u n m it t e lb a r n e b e n e in a n d e r e in g e s e t z t u n d g le ic h z e it ig a b g e le s e n (F ig . 1).
D ie e r h a lte n e n R e s u lt a t e z e ig t F ig . 2. D ie A m p lit u d e n k u r v e d e s K o n d e n s a t o r m ik r o p h o n s is t p r a k t is c h e in e g e ra d e L in ie , d a s M ik ro p h o n a r b e it e t h in s ic h t lic h d e r A m p lit u d e n a b h ä n g ig k e it lin e a r.
A u c h d ie F r e q u e n z k u r v e (F ig . 3) z e ig t, d a ß d a s K o n d e n s a t o r m ik r o p h o n e in e n fü r a k u s tis c h e M e s su n g e n g e e ig n e te n E m p fä n g e r d a r s t e llt . D ie
!) D ie A n ord n un g w a r ähn lich derjenigen, w elche E . M e y e r zur P rü fu n g von L au tsp rechern verw en d ete.
E . M e y e r , E .N .T . 1926, S. 290.
--- ► Hertz
F ig. 3. D ie F req u en zk u rve des K ond en satorm ikrophon s.
3 0 2 Tr e n d e l e n b u r g: Ü b e r S ch allfeld p ro blem e. [ DieNatur- L Wissenschaften E m p f in d lic h k e it is t in d e m G e b ie t z w is c h e n 100
u n d 8000 H e r t z p r a k t is c h g le ic h m ä ß ig . E in e g e w is s e E m p fin d lic h k e it s s t e ig e r u n g w ir d in G e g e n d v o n 5000 H e r t z b e m e r k b a r , d o r t l ie g t d ie s t a r k g e d ä m p ft e E ig e n s c h w in g u n g d e s M e m b r a n s y s te m s . E in e z w e it e E m p fin d lic h k e it s s t e ig e r u n g f ü r d ie G e b ie t e u n t e r h a lb 2000 H e r t z d ü r f t e a u f is o th e r m e V o r g ä n g e im L u f t p o ls t e r h i n t e r d e r M e m b r a n u n d a u f E in w ir k u n g d e r S t ä b e v o r d e r M e m b r a n z u r ü c k z u fü h r e n s e in 1).
D ie in d e m K u r v e n b i ld e in g e t r a g e n e n P u n k t e sin d d ie M it t e lw e r t e m e h r e re r M e ß r e ih e n , w e lc h e f ü r je d e F r e q u e n z n a c h g e r in g e r V e r ä n d e r u n g d e r r ä u m lic h e n A n o r d n u n g d u r c h g e fü h r t w u r d e n . D ie E in z e lm e s s u n g e n s e lb s t s t r e u e n u m e t w a 3 0 % . D ie A b w e ic h u n g e n lie g e n in d e r M e th o d e s e lb s t b e g r ü n d e t : E s w a r sc h o n o b e n b e i D is k u s s io n d e r S c h a llf e ld v e r h ä lt n is s e e in e r g r o ß e n e b e n e n K o lb e n m e m b r a n d a r a u f h in g e w ie s e n w o r d e n , d a ß e in d e r a r t ig e s S c h a llfe ld e in k o m p liz ie r t e s S y s t e m v o n I n t e r fe r e n z e n d a r s t e llt, u n d d a ß in s b e s o n d e r e in
d ie s e r A u s fü h r u n g s fo r m n o c h D u r c h b ie g u n g e n d e r M e m b r a n te ile z w is c h e n z w e i K u p fe r le it e r n m ö g lic h .
M it t e ls d e s R iE G G E R s c h e n K o n d e n s a t o r m ik r o p h o n s w u r d e n n u n a u c h M e s s u n g e n ü b e r d ie r ä u m lic h e V e r t e ilu n g v o n S c h a llfe ld e r n s e lb s t d u r c h g e fü h r t .
B e s o n d e r s in t e r e s s a n t s c h ie n es, d ie r ä u m lic h e V e r t e ilu n g d e s S c h a lle s s e it lic h d e r M it t e ln o r m a le n f lä c h e n h a ft a u s g e d e h n te r K o lb e n m e m b r a n e n a u fz u k lä r e n . E s w a r t h e o r e t is c h a u f G r u n d a ll
g e m e in e r Ü b e r le g u n g e n v o r a u s z u s e h e n , d a ß d ie S c h a lla u s b r e it u n g , d e re n W e lle n lä n g e g r o ß g e g e n d ie M e m b r a n a u s d e h n u n g is t, in F o r m e in e r K u g e l w e lle , a ls o g le ic h m ä ß ig n a c h a lle n S e ite n e rfo lg e n w ü r d e . W ä h r e n d fü r F r e q u e n z e n , d e re n W e lle n -
---*■ Hertz
Fig. 4. D ie F re q u en zk u rv e von B latth a lle rn .
d ie s e m I n t e r fe r e n z s y s te m D r u c k u n d G e s c h w in d ig k e it n ic h t o h n e w e ite r e s p r o p o r t io n a l sin d , s o n d e r n d a ß d ie s e s V e r h ä lt n is g e w is s e n S c h w a n k u n g e n a u s g e s e t z t is t . D ie G r ö ß e d e r S c h w a n k u n g e n is t v o m O r t d e r M e s s u n g v e r s c h ie d e n . D ie Ra y l e i g h- s c h e S c h e ib e s p r ic h t a u f d ie G e s c h w in d ig k e it d e r S c h a llt e ilc h e n a n , d a s K o n d e n s a t o r m ik r o p h o n is t e in D r u c k e m p f ä n g e r ; b e i e in e r Z u r ü c k f ü h r u n g d e r M e s s u n g e n d e s K o n d e n s a t o r m ik r o p h o n s a u f d ie m it d e r R AYLEiGH Schen S c h e ib e b e s tim m t e n W e r t e m ü ß t e d e m n a c h d ie s e (th e o r e t is c h a lle r d in g s s c h w e r zu fa s se n d e ) S c h w a n k u n g b e r ü c k s ic h t ig t w e rd e n , o d e r a b e r m a n m u ß , w ie es b e i d e n M e s s u n g e n g e sc h a h , d ie M it t e lw e r t e a u s e in e r Z a h l v o n M e ß r e ih e n n e h m e n , b e i d e re n je d e r d ie r ä u m lic h e A n o r d n u n g v e r ä n d e r t w u r d e .
D ie F r e q u e n z k u r v e d e s f ü r d ie E ic h u n g e n a ls S c h a llq u e lle b e n u t z t e n B la t t h a lle r s z e ig t F ig . 4, K u r v e I I , d ie a n d e r e K u r v e I g ib t d ie F r e q u e n z a b h ä n g ig k e it e in e s ä lt e r e n B la t t h a lle r m o d e lle s w ie d e r . D ie s e s M o d e ll b e s i t z t e in e n F e h le r in e in e r R e s o n a n z s t e lle b e i e t w a 5000 H e r t z ; e s w a r e n b e i
*) V g l. hierzu eine ausfü hrlich ere V e rö ffe n tlich u n g
„ B e itr ä g e zu Sch allfeld m essun gen “ , W iss. V erö ffen tl.
a . d. Siem en s-K on zern 5/2, 120. 1926.
F ig . 5 - A n ord n un g zur M essung der R ic h tw irk u n g von L a u tsp rech e rn .
lä n g e k le in g e g e n d ie M e m b r a n a u s d e h n u n g is t , d ie A u s b r e it u n g a ls g e n ä h e r t e b e n e W e lle , a ls o m i t a u s g e s p r o c h e n e r R ic h t w ir k u n g , in R i c h t u n g d e r M itte ln o r m a le n v o r s ic h g e h e n w ü rd e .
D ie zu d ie s e m Z w e c k v e r w e n d e t e A n o r d n u n g (F ig - 5) w a r fo lg e n d e r m a ß e n g e b a u t :
E in F e n s t e r d e s L a b o r a t o r iu m s g e b ä u d e s w u r d e d u r c h e in e H o lz w a n d e r s e t z t ; in d ie s e k o n n t e n v e r s c h ie d e n e L a u t s p r e c h e r t y p e n e in g e s e t z t w e r d e n . U m d ie s e n k r e c h te S y m m e t r ie lin ie d e s L a u t s p r e c h e r s d r e h b a r w a r e in e t w a 3 m la n g e r A r m a n g e o r d n e t, w e lc h e r a n se in e m v o r d e r e n E n d e d a s K o n d e n s a t o r m ik r o p h o n t r u g . E s w u r d e n u n d e r D r u c k im S c h a llfe ld in A b h ä n g ig k e it v o n d e r R i c h t u n g d e s d r e h b a r e n A r m e s b e s tim m t . Z w e i M e ß r e ih e n w u r d e n d u r c h g e fü h r t , u n d z w a r b e z o g s ic h d ie e in e M e ß r e ih e a u f e in e n B l a t t h a l l e r v o n d e r G r ö ß e 18 x 24 c m ; d ie a n d e r e M e ß r e ih e w u rd e im
