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rr'rrrv',‘ ’r'fl Tl") I m’": 7‘ "5:1 ‘rxr‘m'n ’4' :71 ‘4“ TTT mm x OI'V‘. ‘7‘ 771‘7‘ T‘T'm r‘
tum ULSUAACL4LL ht luv“; B“ luU bbiouvJLC :tphuo

i

U

Q!

HYRLN fRUL H GQLSSuG

Fobaittefi to the Collm¢e of Scirnce and Arts if

1 _: \_ I '.I_
A‘Kicf !l£;’g.lx11

State University of figriculture and Applie Science

in portlrl filfillment of the requirements
for the floggrne of

‘I -_ .‘1 “N‘

. {‘“I “’7‘ " ”11""? f‘E
i'ALA-J I, J! UL‘ L.)L) F’J'Jk/ I

 

2171". n". '"Ifid‘rw an. -. . :1 "Tm-7m 1r m I fime) '3 ""C Yfllz',‘IT‘)"j
4...“: .J.LL' '-‘I..‘.UL-L\".. pf j-1J.Ut..J. UL L1:‘\.‘ ,1 .Lit.L_I--x..l. - .4 I.)

Lyr<n Paul

0 It . .' ‘ N ‘r‘ . , - 4“, ,—_ ’L'v 1"
T‘e llght 1n all rLtfrroLLcn enters, «Ace;b Dub cano e1
(39, 0? an Ultrrmvnic grebing will be travel; 3 at an an"le

' - - ~ “it -1\ n .m -. ‘ _ 3,.“ , w- 1- __ ‘V-I
LO the 111C"! want bQ'Ul. :19: ‘:1 OJ. blitSB (.1I'1'.C:i.t5 “u f LJG C‘.IIlE)_L\ (:Ifed

. fin. to ‘ . ‘ ~L‘r .. W _‘ 1 1— r ’.V' __ ”H“: _o _‘ .l‘
58 31’] (ugL-lCLLIN'Q I ECG fCIT‘ DIG, ENC 11' brutdwg. LunS -lit‘szi-r-

tiwztlon shows that at low frequencias, the CUJbLHvLLOH anes

17

.'I_ -_ - 1" I"
:e Lileot‘fy OJ. p. v.

‘

“ ~—‘ (- J J" "‘ 4- >1.~.‘ r ' r~ ‘ ,. Q . i‘ l
g: I‘H (It: ,1 [e tric r i)‘ U. l; LDC I] ,_ 11 It? 11”; 'J I.“ C‘- tc.) U U
”5" 1“

r‘ \V _ J“ . __ ”fl 0 ', ‘__ V ' 1' ‘V
1;!11111T‘1 and 1;. .3.r'1"'~'r'1< T8 118‘ uh 71?th 1.01.5. 12L 11 11%“? J J‘LMN‘HC‘P
J-

. ' v.5“ Nr\-- "w r ‘ .3 ‘,‘ . '. ,—. - ~v - ‘ ' ‘ ‘ J- h - -‘ - f I
t1"??? 1.“: 2. In: 3:1 ttrLI'f uCLHJD tJaC per-Tg’ Off 9 8 “MG tr‘ -;'C=J.‘:=CiI.LV(3

H .- f "TM" 4" ' , 3 ---'-~,. -11.. 11”,.“
cr r»J r' 1 (lion. -nt: 1 Ln cc roance n1L1 Due uhCOJJ
n
f.
1‘ ..- 1. _ V 'I‘ *. , r ,\ rr_ 0 J .n ‘ _ ._‘_ , . .' . r“ 4 I. P ‘ L _
0.5. .KLC" {9.1.313 C . H‘JA UUICAIN'H ‘1... . ft L1 111.911 .1. l‘i.’:1‘1~-]_‘3;l(e .1333; (1(1 (1011 L1.l(} UK),

1“ ' ""‘C".L 1‘ ‘0 “V v'3’" ' , \“15\1
J—L‘3(_ tiC n O', LUQLUG (A, t. j\, (‘63-. J-Fxbhru iJI‘C/u‘LLCH

1. “3 (Ill' 3’ Co ‘1]. {1:161 ;:o 30 TI. Era-t1}. Trifle ”1")" hr pCbiC’ll ()f IJibllL
'I 'r"r I-

7” Lrn bre~u3eu0f Soou paves. II. Froc. Inn. .ucam.

U

( )2, u12-20(1935)o

2. Ecigemm’nI, Richard C. Theorie fie 1a ‘it "rfr ction «.16; la
1uriere per 198 ultra-sons. II. Kelv. ,hgsica ficba lO,

lop-,17(l/37).

)-

DTTI .é‘Tjfij ‘ ,.‘.._ ‘N'T {\71 L '_w77T".'1 fit". 3-; :\ 701v- 7-1.3 - - ,.
JL ‘J .‘.Lj.“.i ‘- 0-1.1:; x.-' IMML D... .LuU 011.2ng

L)
p
C

Bv

cl

Eff-Lox PAUL HAGLLBiir-LG

Submitted to tte College of Science and Arts of Michigan

J.,‘-IL

{dc ”niversity of Agriculture and Agplied Science
in pertial filfilluent of the reqwirements

for the devtee of

y)"

uhdtfifi 9F SCIDQUE

Department of rhysics

1936

/

A CKL I (1 t- . LIED G; LEI-3 IS
I wish to express my sincere graditude to
Prof. J. A. Niecemann who sug'ested this pro-
blem and whose ins iration and guidance helped
bring it to a successful Cinclfisicn.
I also with to eXpre 3 my indebtedness to
b

the fictional Science Foundation for nroviding

the funds which mode this work possible.

927. QJW

Table of Contents

Introduction

Theory

EXperimentel Apparatus
Exnewimentel Procedure
Vote and Discussion
Summary

Bibliogr84hy

10

12

21

22

. ..~', .n. ‘ .T
Q1l\ {Jy‘bv I: l‘

l

"1 .‘I I
'7 l1 0837"“ TI n

In 1S3? P. Debte nnq . a. is
2
infl P. Bic evd in France discovered thrt if a

F!

nss 93 through altrescnic fiel” a dif 1r

{reduced utich re cables that dne to a ruled g

~nc.a:t of tie ultrtsenic grating co

wAgu

grating
in the medium.

the light to be diffrcc
“Itras observe a Complex 1
nrider

.1»

once where the grating constant of one of the

is an integral n itille 2f the greting cc;n
and the o“ne where ”he ereting C‘P'ta t, eno h

P
8.. \ .‘

length, cf one nl h no

other In the

V.

W

of the gratings
lines
lires may be observed wiich

In the Cdnd enee

America

rreseonds

particnlr

proflnced by the other

and Lucas

if. .

A . "
b rm cf light

rating. The

to the

ted by a sec nd

»attern of lines,

twe ce" The

ses:

ultrasonic gratings

stsnt of'tmzothe

Q
\’

nce the wave-
:r relation

,
...A

first case dif-

~ill c incide with

grating.

7"

not present

in ti: diffracticn patterns due to either (f the gratin; s
c n idered :egeritelvg there rre known as Cumbination
lines.

Dc ble Jiffr ction may be :btxined in several ways. A
qu*rt e crrstel mifiht be icitr’1 on tho of its odd ifii'onlCS
In this any one obtains two ulti'sénic fields where the n ve-
lenwth of one i: an irtcgsel multijle af t‘e Nevelength of tne
”the: cnd w e7e there is a definite -ese relation be w‘en

the Lwo fields. It is pcssible to obt in doub

1e iiffrrction

this cese since the Ultla nic g:tting has an ex ension cf

pertgns two or three certimeters altng the light beLm: hence

there is SMqle cetcrtunity for the light to be diff“ cted by
cne ul tFTSCDlC grstins anfi then to be reciflr: ctee bf tee other.
Since in a ;olid :ne mar hife shear waves as tell as lengi-
tudinal wzves, dewrle diffracticn may be dbtninefl in tr'nse'rent
Ssiirs in unich 8n ”ltr sonic i;eld has been set U}. Since

tie velocities of the shecr HTVBS an“ the l njituflinel waves

r‘e different there will :e.erell" be two ultrSLenic grrtings

LT
\

ii [ nzv~1rt ecu“ ta llts :znd }ieru:e ciocifiLe Lliiflirfia'titn .
Uen‘ol: eiffr.cti n may also be cbt:inefi bf ”sing the sen-

parate transducers.

. z. _ ,. .° tr" _.. .,- V- . ‘ l.‘ - , .
mwsve UltraSqniC i;ells yIuJuLefl bf tWO ~€

 ~ 1‘: I- , . r- .- ..-. . -_ . - .. e- K + L H- 1., -
‘.,'-_ u] til--.‘ r1399:~'_x-:I.1=.‘.1.I the 1-: _L,!_"t'ie UC Vulfy’ MIG CKHSUUI‘ILS (if (Ale

0
<
'n
L-
if
(D

0T0 ?ltP”S’nlC gratings lnfl~UCFW~nth enfi also t

Lnt::n; a pf the ul_t n‘ brie fLel s and hence the number of

:D

‘ .1 v. ’fi D ‘ ' - r5 g . r c -. (‘ t. u a - f 1 f. a - i“ 1"
d-fLTthlCn ornero. LHLS makes it 3;stzole t; ODt;ln a miner
v rieii of rsttcrns. Lhis mettui fliffe's fren the etier the
' A

r . '-1 ,- " ‘ v - -0 ‘r. -: A (g -5 —-L fl ‘ - , - — — ‘~ ,— - — —‘ ..
31:0 in tfiat tie two yrstings 619 not snparLcsed. inej heme

I")

nrefincefi in this ce‘e in two er"r'- e tanks of liquid.

<'I"5“*‘<ZG“l bf tie fenfrrtfi wltres'nic fiel” , shell be c n idowed

.17’ '. I" I -v"‘ I I“ ". 1‘ ‘ “ ' *- ‘. '1 ‘.~“ '~‘ '1‘ I ' I" ‘l 9 T' '~‘-““
lw1,) 0.2 e Vb » IN .nt,_Lthn,tLg(un;n Lif Lu eezgyearxl (n {.4. r <;u
M
’Y
‘. J r‘L _‘ I‘? V‘- .‘l' "- '. ark-I ‘ r‘\\ ]\" u r‘"! ‘ ' ' "‘
anu l.c<r “J u. u. huVluwa Lee and t; o. r itnaseret_f and
, , i‘ ‘ ‘ r -'-' ‘ ' ‘A I" -~ ‘5 ‘* ‘ “x
we: sine: . “s tzie‘e e rlier SUJHlOS med kHLJ bHGh
~ r~ -‘r . v #‘u . . ‘IIV “‘a‘ I“ _l"\_ ' ' 1 V p ‘ fl 1
nwu3 in a rnc-er linlLted lenge cf ireglen i-S enn :2 nd int n-

uities it a terred desirable to stidy multinle diff~acti n

effects .vcr a hide? renje of fregvenciws.

II. THEORY
Multiple diffraction phenomena have been considered in
the C. V. .cman and K. S. Kagendra Nath theory of diffraction

of light by ultrasonic wavws. Since the ultrascnic gratinv

- »
I...)

‘\

has a finite extension slang the lith beam, litFt which has

0

been diffracted by part of the ultrasoni grating may be redif-
frsctcd by succeecing parts of the grating. Each diffraction
proflnce: a Do pler shift in the frcguency of the light equal
t: the frequency of the ultrasonic field. In this we: Raman
and hath were able to exclain the frequency distribution ov-r
the subcomponenfs of a diffraction order.

On the basis of the Raman and Math diffrection theory,

3

. Jwes obtained a theory of double diffraction by two ultra-

L11

sonic gr tings with different grating constants. K. Nagab-

hushsna Wao obtained the same results by extend mg the methods

i
8
of the generalized theory of N. S. Nagendra Nath .
In his paper Fao gives for the angle ékfi»at which fiif-
fr ction lines may be observed the expression

sin nszrfi +$-§: (l)

in pry-1.1011 r,s =0, 11, t2,- - -, Xawavelength of the light and

f * .
A, and A2 are the I-Iavelengths of the first and second ultra-

s nic berms.

One may see from equation (1) that if the second field
is turned off, that is, if s==O, we obtain the eXpression for
the angles at which diffraction lines due to the fir t grating
31 ne may be observed. when both ultrasonic fields are turned

on, the light, after passing through the first grating, will

h

be split into diffraction orders given by the first term on
the right in equation (1). Each of the diffraction lines of
the first grating will act as an effective light source for
‘he second grating. Now the sec nd tenn on the right in equa-
tion (I) givcst no lines produced bv diffr ction in the second
3r2tin3, of Jig} t in “he rth order of the diffraction pattern
of the first ultrasonic grating. These are the so-called
ombination lines.

“"tion (I) is obtained under the assumption that
sin9,+ sine, = sin(9,.+9,)= sin 9,35, tfluich is justifiable
since the diffraction angles are small. (For example, the
angle for the Sth order of a 10 mc/sec. sound field in xylene
with A=5hc31 A is about 1.2 degrees.)

{he light in the rth order of the first ultrasonic grating
will be traveling at t1 e angle 9=arc sin(r'4) to the incident
be“m of light and therefore will be obliquely incident upon
tTe secmnd “ltrasonicv gretfing. It would be expected that the
combination lines corres ending to a given value of r would
produce a pa tern similsr to that produced by diffraction of
an oblisuelv incident beam in a single ultrasonic grating.

6

The theorv of Raman and hath for the diffraction at ob-
lisue incidence predicts that the diffraction patterns bill
be symmetric about the central order; but, as the angle from
the nannnl increases, the intensity of the diffr~ctien pattern
will pass through periodic maxima and minhna. The angles

at which the ma {ima occur are given b/ the exr:rtssio n

sin(9+ ¢ )-Sin¢=tn%‘ (9)

where ¢ is the angle from the normal and n is an ir3er
grrer‘ter than or equal to zero.

‘

in extended study of viffracticn b/ an ultra:onic grating,

of li3ht Lhich is inci1e1nt obliquely has been mezde bgr Otohiko
9,10,11,12
Koncto . ‘his study has MEOJD that the predictions

of the Raman and Hath theory for oblique incidence are v lid

4 1

at low ultrasonic 1r 2 uenci.s. At higher frequencies, newever,

the diffraction natterns are no lmn3er symmetric about the

central order.

rietrv is extlained b] the fact that at higher

(I

’-— D
m
9.1
tn
b
L.

freqnencies the affect bec mes ne of select:Lve or Jr'"3 re-
flection. Richard C. Extenlann teriven a theorv for dif-
fraction of light at oblique incidence bv crnsidcninn the
ultras nic field to h've a structure similar to t at of a
crystal. The the_r;‘f shcxs that Uie intensit f of the diffrac—
tion "a ttern and the de;: be of asymmetry ha e ms} :ima at angles

corre39cnrit3 to the Bri33 an lea, that is, a1u 31es for which

51119: n?‘ where n=tl, t2,° ' °, and that these maxina ae

crem these c: ns or ti;ns we can exiect thg.t at L L ultra-
S1nic frecuencies tie c:1“33inetinn lines for a given value of

r will be synmetric about that order. it h'x3 her ultrcz1nic
frequencies, however, the c n11n1tien lin as for a. 3iven r will
be selectively riflec ted toward the central or er. Che effect
2 ill v :"t' {31‘1““7‘1811Y’ f r1 m showing prec‘mni‘nant1}; the diffraction

the ham n n:‘1 Hath theory at 11-11 frn uencies , through medium

freeiencies to the rredzminsnce :f Bragg reflection at hi3h

6

ultrasonic fre_uencies. nlthough Brave eflecti n mry intro-
Gtce an asymmetrf in the combinatiun lines sbaut the order i-r,
a similar asymmetry occurs for the order -r so 'hst the overall
gettern is symmetric about the central order.

Equation (1) also shows that the postions of the dif-
fraction lines will be unifiectefi DY revs-sing the orfier of
the two ultrr'f11‘11110 531% tings. at fi‘1—‘11i111eizicies for 1:11:10
Raman and Kath theory is agplicnble, the intensities should
also be the same. At hizhe* frequencies the patterns will

. 1 .LL ,. .,... 1 J . .L‘ 1. .2.I..' j..- n ....‘ .-, ,1 1...!“ . 1", "n ,
not oe tnc sane with the grcblugo re dfuefl since ne eiiect

fl
1)- Bl'“ : '5‘

~~ .111)

reflection will be greoter if the Iigher frequency

"5

field is sec:nd, introducing a change in the intensity dis-
trobutien. This gives a Si ple means of illustrating the

effect of Bragg reflection.

III. EALERE—ljlff1».L {4"}: '. 1,1111.)

F31-

1C 01 1131 cal Setup

The ontical :etua which is u ed in this Lork differs
from the sylte1 usuallr used for observing d_iff1m, tie n Fhen—
TMGHQ cnly in that there ire two W tree nic 3r“ tie3s instead
cf the usual ene. see Fis. l. The source of li3ht is a hi3h
ere sure mercury arc r ted at alert 110 watts. The light

4

es thrcrgh a filter Lhich trsnsmits em p the 3r en line

,
4~ k-'\

e 5361 A before illumin ting the slit which nerves as the

efCective 1cu:ce.T1e l1 ht fr 1the slit is collimstefi by

6.5 inch focal length lens; the obiective lens is or 20
inch fecal length. fhe camera, a model V dxakta with its
lens reLove3, proved to be a Lise CJOiCG since its focxl plane

U1 tter pe Mi a side rings ofe GXJOSUFG times and since it
holes a large supply of f’lm.

The Electronic heuipment
The electr: nic e1nionwnt co1s ists of tLo continuous wave

rsdio frequency transmitters. fihe o tpUt of the transmitters
is centinuouslv verieble up to :bout 130 Letts. Frequ ncy

" ‘w u"!‘ V’ r‘-. 1" v'. ' - -. / —- j - 1
messarenents are n1de Lith a Tree do. oZO-A NetbFOMyDU cre-

1

euencv Ieter and Calibrator, Serial ho. 1117, manuffcturei

1
I

0.1

“e Generfl ’10 CO.

V 1',
' Ultroscnic Sedrces
Ike 501111 sources ere i—c t qusrts t1 ansnucers eit1sr
three-fourths inch or one inch square. Since the liq id u ed

is xylene, a NOD-COud“CtOT, the electrodes are aluminum foil

:lLee to the f ces of the crvst l The crystal is moLnted

Suhmkw 4<0_._.n_o m1... m0 mbzmzonzzoo ._ .wE

<mm2<o 1 v.

mzu... m>_._.om_.mo . O
N.E<DO ozoomm uuc
v.24... 0200mm -~._.
thdno hwy—I 1.0
v.23. ._.mm:.._ 1:.

m3: .. _

wzw... oz_._.<2_1_1_oo 1 o
._._..m. 1 m

amp); 1 u.

wzmq mmwzmozoo 1 4
914 >m30mm2 1 .2

 

 

 

 

 

 

 

 

 

 

 

0 «Odd. 5w _._.

 

 

._ o mun.

9
on a system of rods which permits three degrees of freedom
in afljnsfiing its orieitation. In the case of the 15 mc/sec.
qqar 2 it is necenssry BO sis-oack uhe transducer, since at
that fwequencv it is difficult to obtain a sufficient number

J.

of (iffracti n orders.

10
IV. nilE 13LTAL PRUCLDUHE

The procedure for obtaining a double diffraction pattern
berins with the adjushnent of the Optical system. hith the
help of the built-in m gnifier, the position of the camera is
aijusted to five a sh 1; slit image on the ground glassv viewing
pl te. Closing the iris, thas limiting the cross-section of
the incident light be m, helps to incresse he sharpness of
the slit 11:"e In this work the diameter of the iris is
about 5 mm.

Since tFe re chant frequezcr of the s eve al t1 ansducers
is knuwn app unut lv fiie t“"nsm1tt are tuned to this
value. Usually this is sufficient to produCe a usable dif-
fraction pattern. In the case of the 15 mc/scc. quartz and
for others "lich are excited on higher odd hannonics, it is
nece sar" to make a finer frequency adjustment. This adjust-
ment is mslre by v rving the fre muency unti the Optimum dif-
fraction is obtainei. The criterion in all ca cs is that
there be snfficient diffraction; usually this me ns that at
least the 3rd or”r be present.

Using each ultrasonic :reting alone, the orientation of
the czystal is adjusted so that its pattern is symmc ric about
the central orier After both gratings are afljusted in this
way, the Rouble *iffraction pattern is observed. The orienta-
tion of each grating is Very critical; even an a p.metrv which

can h rdlv be detected in the 1 WVJeual pattérns shows up as

mtic able a;wnuetrv in the dcuble diffraction pet tte ern.

Ehen a dcuble diffraction pattern is obtained which is sym-

11
metric about the central order, it is photographed. Photo-
graphs are also made of the patterns for each of the gratings
alone. In addition the frequency of each ultrasonic field

is recorded.

12
V. DRTA LTD DISCUSSIQN
In pres nting these data the figures are prepared in such
that the grouping patterns of the double diffraction are
mfre clerr. 1min lines are extended from the lines in the
photograph of the d uble diffraction pattern. SuperiMposed

on tnese, in neav1er lines, are the grouping prtterns for

the do-hle diffraction and for the trinafivii’ffrhctfons. In

‘

graphs 01 the double diffraction pattern,

‘3

addition to the photo
the photographs of the patterns produced by each gratin? are

included since the? serve as guide: in analysing the double

Throughout th-s Stflflf the wavelengtn of the light is
Shél A and the liind use* xylene in which the velocity of
sound is 3&0 m/sec. The photographs are not all to the same
scale since the? were not enlarged by he snme factor fnmn

the original 3

Each fiwlre shall be 1i1 seiarately'in order to
goint out the effects which are present.
Figure 2:7{8553 Inc/sec.
jk;=3.77 mc/sec.

[311

1:18 grouping patterns 3

‘
II
.'

10W 'hct the combination lines
are symmetric about each of the diffraction orders of the
first grating. 1ne appearance of only the first or er Cwm-
Lination lines about the sec nd orders of the first grating
is due to the low intensity in the urinarv seeind orders.

V.~_. _
fl .-

The lower intensity of the seccnd pri arr orders compared

to the firs primary orders may be seen from the pattern of

13
the first grating alone. These results agree with the Raman
6
(“nil Hath theory.
arm-e 3:14:10.83 mc/sec.
1);: 7.13 mc/sec.
L

gin" patterns show asymmetry in the double dif-

fraction about both the first and sec nd primary orders. The

H.
0‘)

reason that the asymmetry about the second primar; order

¥Jo
U)

greater than the asymmetry about the first primery order
I

flint light in the second primary order is incident uuon the
seeind 3r ting at an angle very near the third Bragg angle

for this Grating. That there is asymmetry about the firqt

L)

‘
I

primary ormer, which is incident at an angle midway between

the fir t and secenl Brag angles of the second grating, shows

1-

.nat the mrxina for rag; reflection are very broad as the
13
tfieory of Extermann predicts.

Figure L: 61.14-19.96 Inc/sec.
.OS mc/sec.

.96 mc/sec.

14 7
bilfz 7 .OS Inc/sec.
1/; 9

1

igure h-a is obtainei by using the higher f eguency

x
| .

sound field for the first gratin" The gr tings are inter-

Do
ch,nged to obtain figure h-b but the Same sound intensities
— ~ ‘ ‘ r-u -.~ -' ‘ . ' .0 . I.
are useu an in figure u-a. Comparison Oi the two patterns

shone that they are not identical. The sec nd arrangement

a reflection. This

U

shows More strongly the effect of Bra;
agrees with theory sjpce Bragg effects increase with increas-

ing freqrency.

11;

...-‘i<§u_re S:1{=%=l0.00 HiC/I‘CC.

\

‘wo ultres.nic fields of the same frequency cre adiwnted

1 ° n.“

to profince the srne diiirnction putteTnS. According to the

Rmnen and Hath theory, the diffiraction pattern due to ttese

I‘I

1e difiraction pattern

I 0 'l
l

4" - ' r" —\ ‘~-~'- — .H —“ ‘n~. P‘ -
two grdtinge to; tter la tee same 80 t-

1

of she field at an amylituue twice as great.

r13 ’ _ _L ‘

The power tu the lirrb transfi cer is ac meted st that the

o
’1
I
U

"L the intensity of the

O
O
\1
U7.
513
*F?
(D
3

r g
(.0
O
P
c

01-1:‘1‘01113 t7 r(_‘»1-1;f;7‘= i t is

seCend s uni field afljnsted to give the ngo diffractien th-
t re, a Lhotogreph is male ”f the double diffrsction pattern
f r ttene tum ultr s-nic gratings. The current thruugh the

. .- -. .° ' f' '_ . rJ . 1 - .- - .v. -
fir-t tv-rmr‘f‘mcer is incre:a:-;err to 1.3 angeres am the eatuern

.L

fer t?ie 5r:tihg :lcne i3 gfictcgrxphed. 2 congrrison of these

\J‘L

two n:ttcrns in figure shews that they are different. The

speller number of diffrtcticn orflurx in the double diffrsction
pattern 113143;“ be (3191: int—3:" by selective 1‘ 1.1801311 11. Li
the diffraction orders of the fir.t gr tinu will be incident

. .1._ ,. i ‘ ‘,.Jv°y, .. °,. 1. .m *3 m-.. «V. - ,~ -
Ugon tue 390 no “I thr at r~Ciaciy bHe prnbb adulos Hf tue

5- —<

seccnd grating: LH-S there will be reflection back to ;.d the
cent/1'51 (*I‘fief-kr'.
Figure 6: 3.1{=l}.:.27 Inc/sec.
1/2“.- 9.21‘g Inc/sec.
b. The light is now obliqaely ihcidcnt on the
fl'f'.‘ t grrtftig in order t” obtn'n {greetrtr in-
tetsity in t’e ‘igter diffractimn orficrs.

739 “reiting nrttn he ebrut the f'~nt

C) J

tr ;5 urxg; r €lvcti n even though the ergle of incidence

15
is quite different from the Bragg angle for the sec.nd grating.
TVis is explaired by the fact that the Bragg maxina are broad.
Figure é-a Show: that for the sec nd primary 0rd rs the Combi-
nnti n linen toward he outside are stronger than those toward
the central orfier. In iigure 6-b tnis is shown more clearlj.
TLis asvmmetry is Op osite to the asymmetry produced by frcgg
reflection. No explanation for this effect can be given frnn

the c ncidcraticns which hrve been presented in this paper.

16

_-I.III-
I-
lllllll

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2: Double Diffraction at Low Ultras-tilde Frequencies.
14.15.58 Inc/sec.
14:3.77 Inc/sec.

l7

-IIIIII-
Ill-III..-

 

   

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3: Double Diffraction at hcdium
Ultrasonic Frequencies.
“WT-10.83 Inc/sec.
1/“: 7.13 Inc/sec.

18

b ,

 

Ckwp'r13(p Of the bttterflfi groiucefl by errnngements a. and b.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7.1.};1‘1'9 Lean/f5 9.96 we soc

14: 7.05 EEC/35c,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Eifiufe b-b: The or‘er cf the ficlfis is reversed fer thrt of
512311759 "—61, the i1"v.7;.v.*:ns:7_7;.ie s raga-.531 3,7,9 same.
14:7.05 mc/s:._~c,
1439.96 ICC/SOC,

ii.

iv.

19

 

Fir
i.
ii.
iii.
iv.

  

;ure 5:”: 1/2- :l0.00 Inc/sec.

First grating with transducer current of 0.75 angs.
Second grating adjusted to give the same pattern

as the firet.

Double diffraction pattern of the first end second
gratings. '

First grating with trensducer current of 1.50 3 us.

i
.L

20

. _ A

    
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6-a: Double Ciffroctinn m” high ultrescnic frequencieS.
'14E=1L.?7 mc/sec.
1/2.: 9, 2.); Inc/sec.

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T“ 0
I

ngure 6-b: The first grating is now at a smsll angle to the
inci”ent light benm in order tn obtrin the highvr
diffraction orfivrs.

21

VI.:31£CET

fhe date which are presented in this study illustrflte
thnt druble diffraction by two ultrasonic gr tings can be
eXplcined bf c nsidering the diffrcction orders of the first
gratirg to be effective light sources for diffracti n by the
sec nd ultrasonic grating. Since the diffraction orders for
'te first grating will be traveling at an angle to the inci-
dent been, they will be incident obliquely upon the sec nd
grating. At low fresuencies the effects are in accordance

6

with the Vanen end Kath theory for obliuue incidence. it

‘5

higher frequencies selective or ragg reflection till appear
13

as predicted by the theory of Extermann . At high frequency

there occurs an asymmetrv in the c mbination lines so that

tte diffraction is stronger rucv frfin the central order.

f‘is is not cxnlained bv either theonv. Further investiwation
J. - I b

:t Vigi ultrasonic freouencies is necessary t; clarify this

VII.

10.

ll.

13.

.' .‘

Uehye, P. and r. V. 3e rs. (n tee 33c 2t er; n31 of Iigmit
upersonie Caves. Proc. Tat. Aeau. Sci. 18,1;OO-l}(1932).

. "- "“ " ' " ""VI " '. ‘4 (F! V" ‘: fns rw
Lucas ’ R. Ell-K? P . quvf'l‘t“: . 1-. (,"lVUllL-L‘J 1’1 0;. I‘U'C UL...) Oi ' tLKLI.‘ Cu
fl '7‘

a o O ’- 3 ‘ _‘ _ _ I. (w _ _ J- r 1" V _ -. _ R ‘ ‘T‘_ ‘0
“es L” 13cc swu-is a Gee three Plu"uubwUfU3. U. n. (raris)

1911, 213d -u.(l§ 32).

Ber 3menn, L. and E. Fues. Uber gleiehzeiti 3e Raman-Bengxns
an neareren Ultraschalldellen. Z. Ph31'k 109, 1- 13(1938).

Rae, h. A. Govinea. Diffraction of Light by Super 059 ed
A ’GO

1’ . v _ - " J ~ 1 ,-‘ ~o O _ r
tltrasenie Javes. tree. Inn. L080, JCI. o, 6-10(l;3o.

rt1.s r thy, S. and Harkrishen Singh. Diffraction de la
mixiege par deqx faisceaux d'Ultra—sons. Ann. Phys. 9,
fly) r’
0“ (19211) 0

U) C” :1)?!

T“

Enmen, C. V. and E. S. H. Kath. 1;e Diffr'ction of Light
by High Frenueney Sound nevee. Pe:ts I and II. Free. Ind_.
Aeafi. Sci. (L)2, h06-20(l935), Parts III and IV, ibid. 3,
75-8 Ud: 119-125(1/36).

Rae, K. Yagahhushana. D1fframet1on of Li3ht by Ultresenie
raves. Free. Ind. fiend. Sci . 8, '12'--3n(l""n

Hath, N. 3. T‘Ié’,;.ger1(‘:3-a., The Di; "fr 301-101 of Lig‘lt by High
Fre“wenej Seunfi Hives. Gener ”Ii If} R'IGOT}. Proc. Ind.

”CL. x}. 301. (1.1)11, 222-112(1930).

Tomoto, ctchiho. Versuehe fiber die Beugung fies Lichtes an
Ultrasehallwellen. II. Versuehe fiber die Lichtbeugung an
Ultrasehalluellen hei schiefer Inzidene des Lichtes. Free.
Ihys-hath. Soc. Jap. 3rd Ber. 19, 26h-70(l937

Uomote, Ctohiko. Intensitfitsv rteilun3 des Lichtes in den
an fortschreitenden Ultraschallwellen in Flussigkeiten
erzeugten Beujnngsspthren. Free. Phys-Kath. See. Jap.
3rd fiCP. 22, BIL-20(15h0).

Hometo, Ctotiko. Stu ien uber fiie Bengang Vun Lieht an
Ultraschallwc llen. I and II. Free. ths-hath. Soc. Jar.
3“6 Ser. 2}, 390— LOO, 613-3 9(19h2 ).

Nemeto, Otohiko. Diffraction of Li3ht by Ultrasvuic'finvec
Ft Cblirue Incidence. Burl. Kebrycsi Inst. Physical fies. 2,.

78-85(1952)0

Extennenn, Rich: J C. Theorie de la diffr“ction de la
" ‘ ' ‘rr
11n3_ere par mes ultra-sens. Il. nelv. 1/ ica Aeta 10,
1&5-<:l7(19 37)

' gufxmwmni. m2.

 

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