electro-acoustic transducer efficiency

8/13/2019 Electro-acoustic transducer efficiency

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THE ELECTRO-ACOUSTIC EFFICIENCY OF A MAGNETOSTRICTIVETRANSDUCER

byD. Srinivasan and S. S. Srivastava

Indian Naval Physical Laboratory, CochinABSTRACT

A vane type radiometer has been constrtlcted in thelaboratory for measuring the radiation pressure due toacolxstic waves from a magnetostrictive transducer. A methodbased on the use of this radiometer is described for calibrat-ing underwater applications.Introduction

In the course of our investigations on acoustic cavitation in liquids, i t wasfelt necessary to develop a method for calibrating the m.agnetostrictive trans-ducer in terms of its acoustic pressure output. For this purpose a vane typeradiom-eter was fabricated to measure the radiation pressure due to the acousticwaves from the transducer and to calculate the acoustic intensity. Measurementson the electro-acoustic efficiency carried out on a window-type magnetostrietivetransducer which was driven by a Mullard Ultrasonic Generator are reportedin this paper. Some results on the onset of acoustic cavitation in water and onthe resulting spectrum of noise due to the cavitation bubbles are also discussed.Theory

A considerable amount of literature 1 2 exists on the theory of radiationpressure and its use in measuring acoustic intensity. A window-type magneto-~t~rietiveransducer can be treated as a square piston-like vibrator, the radiationfrom the rear face of wh'ch is rendered nrgligible by suitable absorbing pads.The magnitude of the acoustic pressure x at a point on the axis of the soundbeam is given bywhere

a=the length of the side of the transducerv =the particle velocity amplitude at the transducer surface

=wavelength of soundD=distance of the point x from the transducer surfaceC=velocity of sound in mediump=density of the medium

The acoustic intensity is related to the peak acoustic pressure p by theequation I=p2/2p; IFrom equation 1)and 2) one can obtain an expression for the acoustic intensityIx at a point on the axis of the beam in terms of V Since the intensity I, a t


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one obtains, I in terms of I by combining equstions (I), 2) and 3).Thus C2DaI. = - a4v2 swhere is the frequency of the sound wave. 4Now the intensity z at different points on the axis of thc sound beam canbe calculated from measurements of the radiation pressure p exertrd on aperfectly reflecting plate which is numerically cqual to twice the m,ean energydensity in the medium. All the quantities on the right hand side of cquation 4)can be measured; one thus obtains the acoustic power output from the trans-ducer.easurementsBiquard s method4 of measuring radiation pressure was adopted in our

expariments. The apparatus is essentially a kind of a torsion balance carryingon one side a vane on which the sound beam, is incident and on the other asmall.balancing weight. The vane is made up of two parallel thin circular metal foilsenclosing an air gap between them. The air gap makes the vane a perfect reflectortothe sound beam. The vaneis suspended from. a torsion head, by a finenichrome wire which also carries a reflecting mirror. It is shielded from aircurrents by a glass tube. A thin mica wiqdow, interposed in front of the vane,protects it from being disturbed by the hydrodynamic flow of the liquid causedby the vibrating source. The rotation of the vane is measured by the usual 1am.pand scale arrangement.The magnstostrictive transducer supplied by Mullard is of the window-typeand has a resonant frequency of 27 . 5 kc/s. I t was driven by a Mullard R Fgenerator capable of delivering 250 watts of electrical out,put. The transducerwas placed in a large tank of water in which the radiometer was set up at a knowndistance with i ts vane on the axis of the sound beam. The deflection of the spotof light from the mirror attached to the vane was noted for different gain settingsof the RP generator. The experiment was repeated by altering the distancebetween the vane and the transducer. The R F current through the trawducerand the RP voltage across it were also measured.I n order to reduce the observed data in terms of pressure, a second expcri-ment5 was parformed to determine the constant of suspension K, which isdefined as the acoustic intensity required to produce unit deflection on the scale,placed at a known distance from the suspenqion mirror. Bor each position ofthe vane, the acoustic inte~sity as thus de terened for various gain settingsof the ultrasonic generator and the acoustic power output was calcula,ted. At27 5 kc/s, which is the resonant frequency of the transducer, the equivalentcircuit consists of an inductance L in parallel with resistance R both of whichcan be obtained from impedance measurements. The phase factor insuch acircuit works out to 0.995 . Therefore, the electrical input to the tran~ducer asgiven by the product of the R F current and the transducer voltage. The electro-acoustic conversion efficiency was then com,puted for the different gain settingsof the ultrwonic generator.Discussion


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bi DEFEN E s c i m c E omtNa 35plotted against the gain settings of the generator. The vertical lines in thecurve denote the dispersion of values of the acoustic output from the mean.This scatter of values is partly due to the fluctuations in the electrical input(which are similar), and partly due to the fact that the vane does not come toosition but merely oscillates over a small range. Moreover, the radio-meter is very sensitive even to the slight variatisns in voltage. These variationsgive rise to a similar scatter in the values of the conversion efficiency of thetransducer, which was found to be 58&8 . The efficiency is independent of thegain setting of the R F generator within limits of experimental error. The trans-ducer was never driven to the extent of producing cavitation, which wouldhave resulted in a lower value of the acoustic i9tensity a t the point of measure-ment due to the scattering by the cavitating bubbles. The criterion for theonset of cavitation used was the appearance of the cavitation noise.

The validity of the equation (4) in the present calculations can be ascer-tained from constancy of the quantity 28 ; for in equation (4), I is equal tothe constant of the suspension multiplied by the deflection 8 and all theother quantities in that equation are constant. In ur experiments the deviationnever exceeded 25 .Measurements on Cavitation Threshold and Noise

If the gain setting of the ultrasonic generator is increased to an extentthat the acoustic output from the transducer exceeds a certain threshold value,cavitation sets in. Till recently observations of visible bubbles had been takenas the criterion for the onset of cavitation. However, a more sensitive methodto detect the onset of cavitation is by the noise of the bubbles produced at thetime of their collapse. The wide band spectrum of the noise which depends onthe acoustic pressure in the liquids is mainly produced by the pressure impulseswhich are generated during the collapse of the bubbles. Since the spectrumextends into the audible range also, aural detection of the cavitation noisehas been used t o determint? the cavitation threshold in the present series ofexperiments. From Fig. 1 it can be inferred that the cavitation sets in tap water

0


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EFFICIENCY O A MACNETOSTRICTIVE TRANSDUCER '-4th a t has been left undisturbed in the ta nk for a number of days when th e peakacoustic pressure reaches a value of 1 .1 2 atmospheres. Iy en ga r an d Richardson6have found a n empirical relation between th e pressure threshold for cav itationexpressed i n dyneslsq. cm an d radius of th e bubble in cms t o be4450PC 0 - j - 0 . 5 ~ 1 0 ~ 5)

From this eq uation the radius of th e cav itating bubble corresponding to athreshold acoustic pressure of 1.12 a t m is foun d to be X 10 cm. A bubbleof a given radius can pulsate in a n ultrasonic beam a t a frequency which ischaracteristic of it s size. If a an d s are respectively th e radius an d surface areaof tlie gas bubble i n wa ter i t will pu lsa te under t h e action of th e vibra ting m.assof the medium pas an d i ts compliance a 3Pys where p i s the density of themedium P is th e amb ient pressure an d is th e rati o of t h e specific hea ts ofthe gas in th e bubble. The resonant frequency f of th e bubb le is given by

Prorn this equation we find th a t th e natu ral frequency of th e bubble ofraclius 7 10 cm is about 47 kclsec. One should therefore expect the cavita-toin. noise to consist of th e fun dam ental frequency w ith all it s harmonics and acor~tinuous pectrum due t o th e shock w ave generated by th e collapse of th ebubbles. The noise can be picked u p by a hydrophone an d it s spectrum analysed.A typ icalsp ectru m of th e noise in t a p water when the acoustic intensity exceedsthe cav itation threshold value is shown in Fig. 2; it however gives only


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DEFENCE SCIENCE JOURNALqualitative idea of the spectral distribution of the c av itation noise. A detailedpaper on the stu dy of this cav itation noise will be presented in a sep arate com-mun:oation.

The a u t b r s thank Shri M. S. Narayanan for helpful discussions. Thanksare also due to Shri C. Ra m a Rao who took some photographs on cav itationnoise while at the Naval Physical Laboratory.

TABLE IVariation of Acoustic Output or Di rent Ga in Settings of the Generator

I I IGain D=18 oms D=25*5crns

.. 0 307 0.21 64.5

160 0.738 0.36 50.2 0.600 0.30 50.2 0.616 0.36 58.6180 1.08 0.56 52.2 0.727 0.40 60.8 0.846 0.56 66.6190 1.27 0.98 56.6 . . . .200 2.75 1.56 57.0 1.75 68.6 2.08 1.42 68.6205 3.41 2.26 2.82 1.56 55.6 ..10 . . .

2?0 .

D=27 cms

Elec- Acous- Effi-trio tic ciencyinput output(watte) (watts)I

References1 Borgnis, E . E.-Rev. Mod. Phys. 25, 653, 1953).2. B ~ r g m s n n , .-Der Ultraschooll, 1956 Edition.3 Swenson, G.-w. -'~ rinc ip les of Modern Acoustics, p. 1124 . B quard, P.-'Coefl3ients de L'absorption des ultrasons par difference

liquides-Thesis d~ Doctorate Paris, 1953.5. Parbhhs;arat;hy, S., Chari, S. S. and Srinivasan, D., Ann Der. Phys. 21957).6 Iyengar, K. S. and R:chard4on, E. G.-Pluids ReporbNo. 57, Departmentof Scienti nd Imdustrial Research, United Kingdom 1957).

electro-acoustic transducer efficiency

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