isolated sections^, or altering the location of the crystals 

 on the plate often will serve to change the frequency of 

 parasitic oscillations, so that they cease to be troublesome , 



It was found that the simple theory developed for slender 

 crystals did not take account of frictional load on faces other 

 than the radiating end, Thus s an array of crystals is imagined 

 as moving back and forth like a piston, but in an actual trans- 

 ducer 9 since crystals are soluble in water, the motor is usu- 

 ally in a box filled with some liquid,, most often castor oil, 

 which serves to transmit the sound to the sound window (usually 

 rubber) and also to insulate the electrodes from each other. 

 The motion of the crystals is such that the radiating end must 

 push the viscous castor oil aside while the sides slip through 

 it Both of these motions absorb energy, and since they con- 

 tribute nothing to the radiated sound, tend to reduce the 

 efficiency of the transducer When the spaces between the 

 crystals are too small, the energy absorbed in moving the oil 

 in and out of such narrow crevices can be very large , Many 

 of these matters are not obvious at first glance because of 

 the minuteness of the motions under discussion Actually the 

 motion of a crystal in a transducer is not much greater than 

 a wave-length of light s and failure to recognize many obscur- 

 ities in transducer performance is traceable to this c 



Wo Po Mason of the Bell Telephone Laboratories developed 

 an equivalent circuit for a piezo-electric transducer which 

 aids and simplifies the task of dealing with a practical de- 

 sign. The idea of an equivalent circuit is old but useful in 

 applied acoustics. The Mason circuit is one to which all more 

 complicated circuits must reduce when applied to this partic- 

 ular case. It is, therefore^ a check to be applied to other 

 circuits, 



Dr, Camp sought to extend this to practical transducers 

 and evolved a circuit, which successfully took into account the 

 finite size of actual' crystals, loadings on all crystal faces, 

 tangential as well as normal ? and the coupling between various 

 modes of vibration insofar as they are practically important. 

 As it must. Camp's circuit included Mason's as a limiting case. 



Even though an equivalent, circuit is of very considerable 

 aid In simplifying design calculations, it still Involves long 

 and tedious work, A small group of computers under Mrs, Alice 

 Keith was set up at UCDWR to make such calculations. 



It proved possible in many cases to devise equivalent 

 circuits whose components were real. It was then possible to 



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