Characteristics of Radiating Variable Resonant Frequency Crystal Systems

Calculations based on the usual one-dimensional theory of piezoelectric rystal systems have been carried out for several particular variable resonant frequency crystal systems radiating into water. Curves are presented showing the (1) power output as a function of frequency for operation both on and off resonance, (2) resonant frequency shift as a function of backing length, and (3) relative band width as a function of frequency. The validity of certain approximations i checked so that the operating characteristics ofsystems made up of different materials can be quickly estimated. The curves indicate that a variable resonant frequency system of crystals all of equal free-free resonant frequency operating with an allowable power variation for fixed applied field strength of 2:1 can have a continuous variation of resonant frequency of about 2.3:1. A system half the crystals of which have twice the free-free resonant frequency of the others for the same allowable field strength variation can operate over a frequency range of about 5.3: 1.