THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
VOLUME 26, NUMBER 2
MARCH, 1954
Measurements
of SoundAbsorption
in AqueousSalt Solutionsby a ResonatorMethod*
O. B. W•LSON,JR.,t a•m ROBZRTW. LEONAm)
Department
of Physics,Universityof California,LosAngeles,
California
(Receive,d
November16, 1953)
This paperpresentsthe resultsof measurements
of the soundabsorption
in aqueoussolutions
of several
salts.While magnesium
sulfateis the salt of primaryinterestin this case,someresultsfor seawater at
(lifferenttemperatures,
solutions
of magnesium
acetate,zincsulfate,and berylliumsulfatearegiven.The
frequency
rangeof the measurements
is approximately
50 to 500kc. Althoughthe resonator
methodused
isnotveryprecise,
it istheonlyknownlaboratory
method
whichisabletogivereliableabsorption
measurementsin waterandwatersolutions
in thislow-frequency
rangewherethesoundabsorption
in theseliquids
is extremelysmall.
EXPERIMENTAL
METHOD
AND
APPARATUS
theoreticalcalculationshowsthat a family of these
a frequencyspacingof about 5.1
kilocyclesper secondfor the caseof the 12-liter waterfilled resonator.Experiment checksthis spacingrather
well at the lower frequencies.
Becauseof the high modedensityin theseresonators
at the frequenciesused,it is practicallyimpossibleto
locatethe desiredsphericallysymmetricmodeson the
basisof frequency
alone.Thus,only the lowestdecay
ratesin eachsmallfrequencyintervalwereused.
HE reverberation
technique
formeasuring
soundmodesexists with
absorptionin liquidshasbeenusedand described
by others, such as Mulders,• Moen? and Tatum and
Kurze? As used here, the method differs in several
aspects,the mostimportantof whichis the useof single
resonantmodesof the sphericalresonatorin the 30-kc100-kcrange.Tamm andKurze• haverecentlyreported
theiruseof thistechnique
in the 5-kc-30-kcrange.
A smallpiezoelectric
crystaltransducer
attachedto
the wall of a liquid-filledsphericalresonatoris usedto
excite one of the natural
modes of the resonator until
the soundintensity reachesa sufficientlyhigh level.
The transduceris then switched from the exciting
amplifier to a receivingamplifier. The soundenergy
level in the resonatornow decaysexponentiallyat a
rate determined by the energy lossesin the system.
A high-speedpower level recorder which plots the
logarithm of the decayingreceiver output voltage
against time, yields a straight line decay curve, the
slopeof whichis easilymeasured.If the lossesof sound
energyat the walls and supportsof the resonatorare
negligible,the decreasein soundlevel resultsonly from
the absorptionof the soundin the containedliquid,and,
thus, this decayrate is a measureof the soundabsorptioncoefficient
for the liquid.The decayrate, in decibels
per second,divided by the soundvelocity yields the
plane wave absorptioncoefficient,in decibelsper unit
INSTRUMENTATION
A stable, variable frequencyoscillatorprovides a
sourceof signalswhich, after amplification,are applied
through a relay operated double throw switch to the
transducers attached
to the resonator wall. With
the
switch in its second,or rest position, the transducers
are connectedto a high input impedance amplifier
which servesas an input circuit for a model RAK-7
communications-type
receiver. The audible output
signalfrom this receiveris then recordedas a function
of time by a high-speed
powerlevel recorder.Various
changesin electricalconnections
foundto be necessary
(to avoid receiver overload, for example) are synchronizedby a suitablearrangementof switchesand
relays.The resultingrecordingson waxedpaper tape
are thenplacedin a slopereadingdevicewhichenables
directreadingof the soundlevel decayrate in decibels
per second.
of distance.
About 50 decibelsof the sound level decay is also
In practice,for the caseof pure water which has a
observableon the screenof a cathode-rayoscilloscope.
very smallabsorptioncoefficient,the lossdue to propagation of sound in the walls is not negligibly small. The signalis passedthrougha logarithmicamplifier
and rectifier, and the dc voltage from this device is
Energy lossesalso result from shearingmotion at the
boundaryif the excitedmode of vibration has particle displayedagainsta linear time baseon a cathode-ray
velocity componentswhich are tangential to the walls;
this is reduced by the use of nearly spherically symmetric or radial modes of vibration
in which the motion
of the fluid is always normal to the resonatorwall. A
* Supported by the U.S. Office of Naval Research under
Contract N6onr27507, Project No. NR014-302.
• Presentaddress:SoundriveEngineCompany,LosAngeles28,
tube. The use of an attenuator in the log-amplifier
input circuit and timing markersenablesthe calibration of this system.The visible display is helpful in
locatingresonantmodeswhichhavelowestdecayrates;
the high-speedlevel recorder is then used to give a
moreprecisemeasurement
of the decayrates.
RESONATORS
California.
t C. E. Mulders,Appl. Sci. ResearchB1, No. 3, 149 (1949);
B1, No 5, 341 (1950).
l C. J. Moen,J. Acoust.Soc.Am. 21, 62 (1951).
aG. Kurze and K. Tamm, Acustica3, 3448 (1953).
223
Round bottom Pyrex boilingflasksof commercial
variety were convertedinto satisfactoryspherical
resonators
by reducingthe lengthand diameterof the
224
O.
B.
WILSON,
JR.,
AND
R.
W.
LEONARD
tion during this treatmentis made up afterwardby
additionof freshlyboileddistilledwater.Boilingof the
liquidat atmospheric
pressure
withoutsonicexcitation
producesadequate degassingbut results in much
greaterliquidlossesdue to evaporationand thermally
40O
inducedvolume changes.
EXPERIMENTAL
RESULTS
AND
OF THE DATA
TREATMENT
Figure 1 presentsa typical exampleof the experiF-O
IOO
ZOO
FREQUENCY
400
KC
Flo. 1. T.xqaical
experimentaldata for pure water at two
mentally observed absorption in pure •vater. The
apparent amplitude absorption coefficient a was
calculatedfrom the lowest observeddecay rates in
eachfrequencyrange.
It is to be noted that the observed values are some-
temperatures.
The unitsfor a/v2aresec2/meter
ß10's.
what largerthan the currentlyacceptedvalue due to
wall losses.An approximatecalculationof the wall
neckin a glass-blower's
lathe. A supportsystemfor the lossesassumingonly sphericalwavesaccountsfor only
resonatorconsistsof three pairs of 0.01-inch diameter
about one-third of the discrepancybetween the
steelwireshungfrom aboveon a ring havingthe same servedand acceptedvaluesof a/v •. It is believedthat
diameter as that of the resonatorand held together the remainingdiscrepancyis due to shearlossesat the
underneath the resonator by a thin brass ring. To wails of the resonator and that an anomalous behavior
prevent absorption of sound by the surrounding
in the absorptionin water is not indicated.
medium, the resonatoris placed in a vacuum chamber
It was found that the wall loss is, to within the
wherethe air pressureis reducedto about onemillimeter
accuracyof the measurements,
independent
of the value
of mercury.
of the absorptionin the liquid. It is convenient,then,
to deal with the "excess" sound absorption in the
One or moresmall,45ø Z-cut crystalsof ammonium solutionswhich is obtained by taking the difference
dihydrogenphosphatecementedto the resonatorwall between the observedabsorptioncoefficientfor the
serveas both a soundsourceand as a microphone.It solution and that for water at the same frequency.
was foundconvenientto usea conductingsilverpaint For the solutionsstudiedhere, the absorptionin the
for the crystal electrodesand for cementingon the
TRANSDUCERS
thin lead wires.
A small disk thermistor
cemented to the resonator
permitsmeasurement
of the temperatureof the sample,
whichmay be variedand controlledby controllingthe
•G
o
oo
5C o
temperatureof the vacuumchamberwall. The temperaturestabilityof the controlsystem(-½0.5ø to IøC)
is sufficientfor the presentinvestigation.
PREPARATION
OF
SAMPLES
The sampleswere compoundedfrom distilled water
and a cp grade of the salt to be studied. The natural
seawater sampleswerefiltered througha fine gradeof
filter paper. Growth of bacteria and other organisms
in the solutionswas deterredby the addition of about
four parts of mercuric chloride per million parts of
sample.
Before measurements
of soundabsorptioncan be
made,it isnecessary
to degastheliquidin theresonator.
This is accomplishedby boiling the sample at room
temperature and reduced pressureand, at the same
time, irradiating the resonatorin an intensesoundfield
whose frequency correspondsto one of the radial
resonant modes. The high-amplitude sound waves
20
,0
5 o•=.00
2
I
50
I
eo
I
ioo
FREQUENCY
,
I
200
I
•)0
400
KC
FIo. 2. Observedvalues of the excesssoundabsorptionper
increasethe rate of gasevolutionby severalordersof wavelength-l0
s as a functionof frequencyfor MgSO4solutions
magnitude.A smalllossof liquidasa resultof evapora- at severalconcentrations
(in mole/liter). Temperature:23ø-25øC.