‘S‘HE EMPEDANCE MET'Hfib AM} ETS
APPLICATIQN TO THE HETERMINATEQN
Q53 Tfifi ACOUgTé‘Z [IMPEDANCE OF
L§QL3§D MEDM

Tlmés: 5M thee SW :35 My 32
MECHEGhN STATE iiN‘i-‘VERSETY
Robert Richard Sfieaum
W503

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MICH|GAN STATE LIBRARIES

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LIBRARY
Michigan State
University

 

 

 

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PLACE IN RETURN Box to remolee this checkput from your record.
TO AVOID FINES returh ori orbefore date due.
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DATE DUE

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ma W14

TIE LIPMD’T'C“ IIZTIIOD- “.TLD ITS ATP LICATION TO TIE
DETERM NATION CF TIE I‘COUSTI C IKFEDAHCE

CF LIQUID MEDIA

By

Rebert Richard Slocum

AN ABSIH ACT

A Ti? ~SIS
Submitted to the College of Science 51nd Arts of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
he requirements fer the degree of
TER OF SCIEICE
Department of Physics

1956

Approved 2‘ A W

 

HE IHPZD‘TCT "”“WPD AID ITS ATTLICA-IOI TO THE
DITERNINATIOT OF THE MACOIST IC IMPE AT 3 OF LIQUID
T-‘ED IA 0

The theory of electroacoustics has provided
methods whereby analysis of tra11sducer performance
may be carried out by measurements of the res ctive
and resistive components of the electrical imped-
ance offered to t‘1e terminals of the trfnsducer.
From plots of t11e impedance components vs. free ucn-
cy, quantities proportional to t”; 1e acoustic imped-
ance of the wedium into which the transducer is
operating can be derived. After empirically deter-
mining the apprOpriate constants of the transducer,
the acoustic impedance of the medium may be derived.

’5

Examples 0: t

1

as kind of in:_ormation ti 1at may
be obtained about the transducer performance char-

acteristics are given, and the results of meanu“e—

f’)

ments on liquids are presenter. The underlrirc
.. \2

.134-
.a'.

theory is outlined, an a discussion 0- the general

Lu

utility of the impedance method is inclurei.

Robert Richard Slocum

THE IMPFDANCE METHOD AND ITS APPLICATION TO THE
DFTTRMINATION OF THE ACOUSTIC IMPEDANCE
OF LIO UID MFDIA

BY

Robert Richard Slocum

A THESIS
Submitted to the College of Science and Arts of
Michigan State Universitv of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of
MASTER OF SCIENCE

Department of thsics

1956

AC 32101-552334: _- :2-

I wish to mun: Dr. E. A. Modems; ‘1, wh
suggested the development of this method, for his
guidance and many sugfjostions duri ngf, tho develOp-
mont of the equipm .71t, but more especially for

his Lmdorstendirr; and encozuesgomont o

R.SM

II.

III.

IV.

VI.

VII.

TABLE OF COKTEIT
Page

INTRODUCTION...... ..... ............ 1
THEORY...... ..... .................. 3
OBJECT OF EXPERIHLNT............... l4
EXPERIMENTAL SET-UP & APPARATUS.... l5
DATA............................... 21
CON LUSIONS AND SUG?TSTIONS........ 26

BIBLIO'GRi‘.PI—1Yooooooooo0000000000000. 28

I. INTRODUCTION

The impedance method is a familiar one in the field
of acoustics. The term 'motional impedance' was first
introduced by A. E. Kennellv and G. W. Pierce in 1912,
when they were studying the variation of impedance with
freouency for a telephone receiver and discovered that
the electric impedance could be influenced by the motion
of the coupled mechanical svsteml.

The impedance concept was introduced into mechanics
and acoustics as a result of the similarity in form of
the mathematical equations for acoustical and mechanical
vibrations with those of oscillating electric circuits.
Its introduction proved invaluable to the analvsis of
transducer performance and facilitated improvements in
transducers by leading to the develOpment of a compre-
hensive theory of electroacoustics.

The impedance concept carried over very directly
into ultrasonics, where it continued to be of vital
importance in transducer design and theory. Radiation
resistance, motional impedance, and impedance matching
are important considerations for anyone working with
ultrasonic transducers.

Pecause the motional impedance of a transducer is
affected by the medium in which it is Operating as well
as the manner in which the crystal is mounted, and since

a change in the motional impedance in turn causes a

variation in the electrical impedance offered to the
generator at the input terminals of the transducer,
observations of the electrical impedance lead to a
knowledge of some of the important preperties of the
media being irradiated. This studv utilizes the imped-
ance method for the measurement of the characteristic
impedance of various liquids.

The theory will be outlined in Section II, and its
Specific application to this problem and the apparatus,
and some of the problems involved, including its limit-

ations, will be considered subsequently.

II. THEORY

As has been pointed out, the study of equivalent
circuits and the analogy between electrical and mech-
anical oscillatory phenomena has led to the deveIOpment
of the theory of electro-acoustics. By means of this
theory it is possible to represent electro-mechanical
transducers by a single form of equivalent circuit.
Although such a representation by a single equivalent
network allows maximum generality for application of
theory to different cases, it has become common practice
to use different types of circuits for different trans-
ducers, on the assumption that some networks are physi-
cally more meaningful than others. Here the discussion
of transducers will follow the more general method, in
which the transducer is considered as a four-terminal
network.

Following the theory given by Hunt2

, we consider a
transducer as a four-terminal network, with two terminals
representing the electrical input coupled through a
"black box" element, which represents the general con- ,
version of electrical to mechanical energy, to a mech-
anical circuit of a single degree of freedom (figure 1).

0n the electrical side, a current I flows through
an electrical impedance 26, with a voltage E across the
input terminals; on the mechanical side, there is a

velocity v, a mechanical impedance Z , and a force F

m

across the output terminals.

Two equations are needed to describe the behavior
of this system: one in terms of the electrical quantities,
including the reactions caused by the motion of the mech-
anical system; the other in terms of the mechanical var-
iables, as well as any mechanical reactions due to the
currents and voltages in the electrical network. The
symbols T.m and Tm, represent "transduction coefficients",
denoting electromechanical coupling. Assuming a steady
state, with time appearing in the form eiwt, the equations

are
E - 28.1 '. Tem'V

(1)

F - Tme'I + Zm°v

Some important prOperties of the electromechanical
interaction can be displayed by observing the driving-
point impedance appearing at either pair of terminals.
The electric driving-point impedance at a terminal pair
is defined as the complex ratio of voltage across the
terminals to the current in the terminal pair, when all
other electromotive forces and current sources are
suppressed. Putting F-O in Eqs.(l) and solving for I

in terms of E, we get

E’ (T' T’ )

The mechanical driving-point impedance is similarly

found to be

Equations (2) and (3) show the usual electrical
and mechanical impedance with an additive term contain-
ing the transduction coefficients. These extra terms
represent a modification of the impedance caused by the
presence of a bilateral electromechanical coupling. The
additive term in Eq. (2) indicates the modification of
the electrical impedance by the motion in the mechanical
system; this term, (- TmeTgm) - Zmot, has been given the
name of "motional impedange".

Then Eq.(2) may be rewritten to include this defi-
nition in the form Zee' Z. + zmoto where Z. is the
"clamped" or "blocked” impedance, measured when the
mechanical system has in some manner been prevented
from vibrating. Since the motional impedance, Zmoto
is directly proportional to the negative product of the
transduction coefficients, its nature will depend on
the size of these coefficients and whether they are
real or complex. However, the general behavior of the
motional impedance, especially its variation with fre-
quency, may be studied by considering the behavior of
the mechanical admittance ym, since Zmot'('Temee)/Ymo
where ym - l/Zm.

If the mechanical impedance Zm is written in the

generalized form Zm - rm + j‘UIm * __l__ ' rm * 31m:
jwcm

where the quantities rm, 1m, and cm refer to the mechan-
ical resistance, mass, and compliance, respectively,
~‘and xm denotes the mechanical reactance, we see that

the variation of this impedance with frequency may be
exhibited by expressing Zm as a vector from the origin
in the complex xm-rm plane. In general both the length
and phase of this vector will vary as the frequency
changes, and the tip of the vector will trace out a curve
which is Called an ”impedance locus". If rm is not a
function of frequency the impedance locus will be a
vertical straight line at a distance rmfrom the origin.
The phase angle is zero at the angular frequency of
mechanical resonance,CUO2 - l/lmcm.

If a similar plot is made of the mechanical admit-
tance, 7m! the admittance locus is a circle, which is
just the geometrical inversion of the straight-line
impedance locus. This admittance circle has a diameter
of length l/rm. Since Z3, is real at mechanical reso-
nance,ym is also real when.a)02 - l/lmcm (figure 2).

If we call the frequencies for phase angles of7T/2
and -7T/2 radians al'and cu" (the quadrantal frequencies)

 

I l -_ I [-0) 2
respectively, we may write rm --w 'm+w' cm' w 'm [(0.20 ]

d - +-afW - —J——‘=<v"l lzéflgi
an Tm - m w» cm m w "2

From these relations it can be shown that w'w'Ewo‘

Further, the damping of the mechanical system, rm/Z 1m:

wit—wt
is found to be I‘D—'2 'm" 2 , and the mechanical quality

factor cm, ”I : Qm= 600
I'm — (Lin-(d

Thus, measurement of the resonance frequencies and
both quadrantal frequencies gives enough information to
determine uniquely the relative values of rm, 1m, and
cm. Only relative values are so obtained because meas-
urement at the electrical terminals gives the admittance
locus multiplied by the scaling factor (-Temee). This
product of the transduction coefficients may be consid-
ered as a vector operator which both alters the scale
and rotates the diameter of the admittance circle
about the origin by an angle denoted by 2/9. It also
serves as a units Operator, converting the locus of
mechanical admittance into a locus of electrical im-
pedance.

The electhical impedance vector, 2e! may also be
represented on the complex plane. Since Zee - 29+ Zmots
the plot of the total driving-point impedance, Zee’
will be a combination of the motional impedance circle
with the tip of the blocked impedance vector, 28, as
its moving origin, resulting in an impedance Icon of the
form shown in figure 3.

Such loons occur in the vicinity of the resonance
frequency, and smaller loons appear at the harmonics,

with the possibility of parasitic modes giving rise to

loops also.

"When the mechanical system is blocked the electrical
impedance, 2., and its frequency-variation can be measured
directly. After making similar measurements when the
crystal is allowed to vibrate freely, the motional imped-
ance may then be found by subtracting Ze from Zea at each
frequency. Since it is usually impossible to block the
motion of the crystal completely, it is necessary to infer
the shape of the blocked-impedance locus by smoothly join-
ing the measured values of Z. made at frequencies far
above and far below resonance, being careful to avoid
the region of a harmonic mode. This interpolation may
be done most easily if the values of R. and X, are
plotted in rectangular coordinates with frequency as the
abscissa. Then direct subtraction gives the coordinates
of rm and xm for each point of the motional impedance

locus:

In this way the motional-impedance circle may be
drawn and its diameter and resonance and quadrantal
frequencies found directly. In addition to being able
to calculate the values of rm, 1m! and cm from these

diagrams, it is also possible to find such quantities

83 the mechanical quality factor, Qm’ the mechanical

power delivered to an external load, the effective effi-
ciency,77, of conversion of electrical power into useful
mechanical power, and the maximum efficiency of power
cenversion.

Now let us consider a specific equivalent circuit
for a piezoelectric crystal. An equivalent circuit is
a combination of R, C, and L elements, which, when sub-
stituted for the element in an electrical circuit, will
exhibit the same electrical properties as the element
itself. The equivalent circuit which is now universally
accepted for a piezoelectric transducer3 is the one
shown in figure A, where the series arm R, C, L is re-
lated to the mechanical elements resistance, compliance,
and mass, respectively, and the parallel condenser, CO,
expresses the preperty of the crystal as a capacitance.
This equivalent circuit is treated in detail by Cady3,
Mason“, Vigoureuxs, et.al.

At mechanical resonance, L and C have equal magni-
tudes but Opposite phase, thus cancelling out, and the‘
equivalent circuit reduces to a simple R-C network. It
is important to note that the circuit elements in the
equivalent network are considered to be strictly constant
over a narrow range in the vicinity of a resonance, and
that similar circuits apply near each of the harmonic
modes, R, L, and 0, taking different values for each

harmonic.

If a coil whose reactance at the resonant frequency
is of the same magnitude but of Opposite sign as the
reactance, l/hJCo, of the element CO, is inserted in
parallel with the crystal, then the resulting network
will show only the pure resistance. A measurement of
this resistance offered by the transducer and coil at
the electrical terminals at the frequency of mechanical
resonance will permit the evaluation of R of the equiv-
alent network. However, this resistance, which corre-
sponds to the mechanical losses of the crystal, depends
on the method of mounting and the internal losses in the
transducer as well as on the loading medium. If the
internal losses and those due to mounting were negligible
compared to the radiation losses into the load, measure-
ment of the resistance at resonance would give directly
the characteristic impedance of the liquid being irra-
diated. An arrangement where these approximations are
quite good can be practically realized for a free crystal
operating in a highly absorbing liquid. A more accurate
way of eliminating the effect of the internal and mount-
ing losses is to make a resistance measurement at resonance
when the crystal is Operating into air, and another
measurement when it is Operating in the liquid under
study. This corresponds to having two equations from

which the mounting and internal losses may be eliminated.

lO

The common liquids behave like pure resistance,
but some of the more viscous ones exhibit a reactance
component in addition to the resistance. In such a
case one may evaluate the reactance component by meas-
uring the change in resonant frequency of the crystal
from the unloaded to the loaded condition. Actually
it appears in practice that one may consider the
unloaded frequency as that measured for the crystal
in air, provided the liquids under study are relatively
viscous.

Thus it is clear that the characteristic impedance,
ZO - Rm + 31m, of a liquid may be found by measuring the
change of electrical resistance, 13R. - KlRm, at resonance,
and the change of resonant frequency, Zlf’- KZXm, between
the unloaded and the loaded conditionsé. The constants
K1 and K2 may be evaluated theoretically from the geom-
etry of the crystal and the type of mountingh'é. In
practice these constants are determined experimentally
by carefully measuring ARe and [3f for a liquid whose

characteristic impedance is accurately known.

11

 

 

 

 

 

 

A la —° 0— -
I —Tme—> T
E F
I ‘9—Tem— I
C>* e~43 C>* C)
<——i v——>

Figure 1. General four-terminal network,
valid for all transducer types.

 

9m

 

D='/fm = 9m
Ym = 9m +ibm= I/Zm

Figure 2. Motional admittance circle for r
independent of frequency (vertical
straight-line impedance locus).

12

+Xee

 

 

_k%

Figure 3. Typical electrical impedance
100p (generally non-circular)for
frequencies very near resonance.

 

 

 

Figure 4. Universally accepted equiva-
lent circuit for piezoelectric
transducer.

13

III. O'3JTZCT .7 T’IT'J'I 7'13???

9

Because of the rather general utility of the
impedance method it was considered desirable to
build up sufficient apparatus so that the technique
would be available whenovor it might be noedod for
studios in the ultra sonics lal)oro.tory, in conjunc-
tion with both Optical and pulse methods.

As an example of the knowlod3o that may be
gained by this mothod, the do cision was made to
undertake an investigation of several liquids to
determine their acoustic impodonoos, from'which he
sound velocities may be derived, if desirod. This
wo also done with an eye toward dotcrminin:
whether thoro mi3ht be a sufficio1t time-variation
in the acoustic in~tdcwoo of 033 albumin to make
Toss iblo tlzo development of a method for chockin3
the freshness of 0333 by ultrasonic radiation.

In order to ill: 1stroto tao usof.ulnoos of his
method a wioty of italics 10‘.lS are disployod.
Toward this 0nd two impedance looms (a riot of
reactnnos vs. resist nnco witl1 fr oquoncy as a nnra~
motor) have boon inc ludod. An impedance loop is

useful bo ouso it ran ors immediately visible many

important pfirform once charcctnriotlc of transducers.

14

Another interestin3 practical problem is the
effect of the method of mountin3 on the transducer
performance characteristics, for which the imped-
ance method can give valuable infioreaticn. Dre to
time limitations only one crystal was considered

from this particular point of View.

IV. EXPERIMENTAL SET-UP AND APPARATUS

For all investigations in the vicinity of one
megacycla 3 Brush Hypersonic Generator model BU-Zlh
was used as a source of alternating current. This
oscillator has an output frequency range from 300 to
1,200 kilocyclcs. This frequency rang. is covered in
five stages, involving altcring the coil in the fre-
quency-control tank-circuit. Within the five ranges
the frequency is continuously variable by means of an
auxiliary coil located insidc the main coil of the
control tank circuit, causing small variations of
inductance of the L-C tank circuit.

The measuring instrument per so was a General
Radio domesny R-P Bridge, Type 1606-A, in conjunction
with a Hallicrafters General Communications Radio
Receiver, Mbdsl 31-62 A, which functioned as a null
detector for determination of bridge balance conditions.
The type 1606-A Radio Frequency Bridge is a null instru-
ment for use in measuring impedance at frequencies
from #00 kc to 60 Me. The bridge is used with a
series substitution method for meésuring an unknown
impedance, Zx’ in terms of its series resistance compon-
ent, Rx’ and series reactance comnonent, Xx. The

Iresistance is read from a variable-condenser dial directly

_ca1ihrated in reactance in ohms at a frequency of 1 Mo.

16

The resistance dial reading is independent of frequency,
and reads from O to 1000 ohms; the reactance dial from
O to 5000 ohms at 1 Me.

The important characteristics required of the meas-
uring apparatus are the following:
(1) The oscillator must be as stable as possible in
frequency, the output frequency and voltage being rela-
tively independent of the load. It would be desirable
to have one oscillator to cover the entire frequency
range of interest to the experimenter, but it may be
more convenient to use several oscillators of different
frequency ranges, as was done in this case. The gener-
ator must also be adequately shielded so as to avoid
stray coupling between it and the detector.
(2) The bridge must be a radio frequency type, capa-
ble of a high degree of accuracy over the entire frequency
range of interest, and well shielded against stray pick-up
from either the generator or detector. It is strongly
advisable that co-axial connectors be used for connections
to both the source and the receiver. Obviously the
reactance-resistance ranges must be commensurate with
the corresponding impedance components being measured.
(3) The detector must be of high sensitivity in
order to enable very rrecise location of the balance
point, since this is the quantity of major concern in

this method. It must be well shielded, for the same

17

reasons mentioned in connection with the signal gener-
ator and the 3-? bridge. It must possess a local oscil-
lator capable of putting out a strong, clear signal, and

should have an automatic volume-control switch.

Frequently measurements were made with a U.S. Army
Signal Corps Frequency ther 80-221 J, with a range from
125 to 20,000 kc. The prime requisite of the frequency
measuring device in this application is accuracy. The
meter used here was accurate to 1000 cycles per second.
(see figure 1 for diagram of apparatus)

The procedure for making measurements was the fol-
lowing!

The signal generator was set somewhere in the

vicinity of the resonant frequency of the crystal,

which was Operating into air, This frequency was
measured on the frequency meter, and then recorded.

Then the bridge was balanced with the crystal short-

circuited. After connecting the crystal into the

unknown arm of the bridge, a balance was again ob-
tained using the reactance and resistance dials.

The reactance and resistance were then recorded.

This procedure was then repeated in its entirety

for several different frequencies, until it was

certain that the resonant peak in a plot of re-

sistance vs. frequency had been located.

Next the crystal was immersed in one of the

liquids under consideration and the procedure

outlined above was repeated, step by step. An

example of these plots is shown for a general

case (figure 2.)

Lkasurements were made for several different crys-
tals in each of the liquids investigated. Also some
measurements at higher frequencies were made, using
another oscillator that was available. In general
reactance measurements were not made, since only the
resistance and the resonant frequency were required
for obtaining the acoustic imredance of the liquids.
However, in order to obtain impedance loops, reactance
data were measured in a few cases.

As a rough indication of the effect of the crystal
mounting, measurements were made on an unmounted barium
titanite disc, and then again after the same crystal had
been glued onto a phenolic resin composition board back-

ing on one side.

19

 

 

 

 

 

 

Y

 

FREQUENCY
METER

 

 

 

 

’5

 

DETECTOR

 

 

 

OSCILLATOR
T T
e e ’c
BRIDGE
9 Q ‘c
Figure l.

RESISTANCE

 

Block diagram of experimental

apparatus.

A

 

 

O

 

 

 

AIR

 

 

FREQUENCY

Figure 2.

Typical curves of resistance
vs. frequency in air, and with
liquid load.

20

V. 0’

re
>

Figure (l) is a plot of moasurrd electrical
resistance vs. frequency for a freely vibrating
barium titanate orys ml with a resonant frequrncy
of 1.0911 mogaoyolos por second. The broken curve
is the one which applies to the unmounted crystal.
The solid curve is the same plot for the crystal
when mounted with air-backing in a brass crystal-
holdor of the type commonly used for ultrasonic
investigations of liquids.

Figure (2) is a plot of the measured electrical
resistance vs. the moasurod electrical reactance
for the unmounted one mafiacycle barium titanato
crystal, exhibiting the typical impedance loop
form.

Figure (3) is a plot of ‘ho motional resistance
vs. the motional reactance. The plotted values are
the difference betwoon the measured olcrtric l impwdu
once components and the blocked impedance commononta,
tho lattor boi 3 obtained by extrapolation, as
discussed in roction II.

Tho diameters of tho motional imp d 200 circles-

are inversely froportionsl to ,ho losers of the

P.)
H

cryst"l. fineo the lo its? mes ion was air for
both cases, the decrees, in diameters inflicrtes
cls“rly the losses coused by the mountinfl. Since

’ho quality factor, Q, is relotefl to the hol’-wifl it};

of the lac onant peaks, it is obvious tfint tko mounting
e nsia rsbly lowers tho 2. By measuring tWo imoedo
sore o? tho cr:,st .1 rqfiouqt:d, then “coin whcn in

tho crystal holficr, sni tfien when Operatinfi into a
liqull of known inpoicnce, it would be possiblc to
fietrrni.o tho losses of tho holler.

"‘"nre (4) is a graph of the ”ensure? electri-
cwl scri cs ros istcnec st t? c rnti-resonont frequrncy
$8. the known values-of tho acoustic inpcionco of
two four liqzids in which e"érruueqcs Wrrc ordc. The
eryo‘ol word for to so deto was s two—inch sdusre
barium titocoto of nominol P“O”“Ufij of ono W{~~
cycle oer scoonfl.

4‘

2511.511" to T'ir'nre (4-) 30:”

L J-

-- ~ ,, '7 4-
wi‘uro (p) is a plot a
’- n n‘ ‘- V . Q ‘5 ‘ 1" "
mJuSUPCJcnhB perforncd witd a one merocyclo nrr s conl

emirtz crystal.

.mmfipcsoe eoxomnucao 90% cmam use .Omao
opmsmuap Esanmn oopcsoess poo zozcsoonm

.m> mm %0 poam .H oksmfim

33x02. >ozuacmm h.
9; «9. no; so; mo; no; we;

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Figure 4. Comparison of measured values of the acoustic
' impedance of four liquids with their known values,

taken with barium titanste crystal.

 

 

 

"'5 Jean ENE -_ ‘
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IO.5 \
a PiEANUT on?"
m.

I55 4\\\\i
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pg 00 x 10"
Figure 5. Same as Figure 4, using quartz

25

 

 

 

 

 

 

 

 

I45

'- r “'“',"f YYf'TP-Tv": " 5"", «'577r""-",'“"'T‘TP\"C"
1 . ‘ 1") .,x.‘.."'~'-/ 3' a n"I-“\.J‘-- I.’). ..‘-".’l’-.‘

H}!

inc date shown in Section V, nnfl the experience
coined in assembling eni using the nonsrctus, clearly
point out several important conclusions. Firstly,
the percentage errors in the measurement of the
acoustic impedance of liquids ct s froeuency of onc
megccycle with t' e nrcsoxt opporetuc are so hifin cs
ten percent, rcnierinr; it impossible to determine the
tim"-v"rilt on of eM‘ e.lbumin to better th.?n ten
ncrcent. This cie”rly ca ms insufficiently s our to.
tecer“y t operfornhnce of the no suronontc with
tfie nresefit equipment is vrry leIr rni trou“lescre.
It sIocsrs, however, that it will be possible
in o compnro tivcly short t me, to inern“re the accuracy
to within one or two percent. Chfly, in n p.coer for
the Office of Ecvcl Tesecrchg, reinte'out thet
similar m7 hoi, but oneroting at the much rrerter
”rcoucncy 0:? fifteen meter cycles n r second, is conn-
hle of accuracies as hifh rs one fiercent. Prueticclly
no chances are no sery for extension of the ccuip—
cent reed for this study to the fifteen mcgccyclo
rocion.

For st lice in hip Ily vis~eus liouils w ich

1.1 6.0

"101-: s. M rtwd

GLIJPPCHCG bstwrcn t*c

1..

4- \
resistivc :nd

rcactivs componcnts of the acoustic impcdfincc it

will be necessary to csnstr~

ancncy Hf surin: drvicc
ult:

cnt

qwcncy from air to liquid,

is cxtrcmcly

cyciMs pvr scconfi).

27

tann

is proportioncl to the

small (on the

act a mcrc scnsitivc frc~

is now av liable in the

ascnics laboratory, becsusc tic rcactivc ccmficn-

chance in rcscnsnt fre-
frcqucncy cWrnMc

of a few hunsrcd

1.

3.

4.

5.

6.

7.

9.

10.

11.

Hunt, F.V., "Electro cous tics," Rsrvsrd univer-
sity Press, Csmoridgc, 1300., 1954.

Cody, 'I.G.I" woclcctricity," McGrc w-Iill, Now
York,l +6.11

Rsson, J.P "Pic: ocloc ric Cr"stcls and incir
Application to Ultrasonics," D. Van Nostrc nd
Co., Inc., New York, 1950.

Vi"ouroux, P., "Cu rts V bro tors and Their Appli-
cations, His Mojcsty' s Stationery Office,
London, 1%

line tor, T.F., and Richmrd! I. Bolt, "Sonics,"
JoEIn Iilcy 6: Sons, Inc., New York, 1955.

Roson, J. P., "Tlcctrorccrcriccl Transducers and
Rave Filters," D. Van Lo: trc nd 00., Inc., Row
,YOZQI. ' ., 1 3'2“- 0

mason, J.P., "Shear 310sticity osd Viscosity of
liquids," Boll) mclophonc System Tech. Pulyli-
cs.tions, Monogrcpll 3-145 7.

CSdF. ~.G.. "II c.surcmcnts of Trcnsduccr Incut cod
Output!" ORR, Contrc ct U6 014401, TcsI.: Order 1,
1:3 C11; #01, TGC1‘1. £0th 7:! 3’ 19149:

Cody, W.G., "HcDSI Iromcrt of tlie Specific WPcousiic
Resist an of Liquids," OIT, ControctI 36 ORR-262,
Tos120rdcr 1, II’R 015401 Tech. cht. ! 4,1949.

Cody, II.C., "A Capacitance Bridge for 315,11 Fro-

quoncics," R.S.I., 21 (1950),1002—1009.

Roth,J., "Tic: oclcctric Transducers, " chh. cht.
Lo. 43, Resos.rch Lrsorctory of Eloctronics,

Lc.ss. Inst. of Technology 1947.
“ry,' M3 ., "low Loss Crystcl Systoflis, J.A.R.A.,
.23.. (1 9+9). 29.

28

.171. ”'55 '

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