Frequency dependence of the ultrasonic parametric threshold amplitude for a fluid-filled cavity

The excitation of fractional harmonics in a liquid-filled cavity by ultrasonic waves was described previously as a parametric phenomenon [L. Adler and M. A. Breazeale, J. Acoust. Soc. Am. 48, 1077–1083 (1970)]. That is, by driving a transducer at one end of a fluid-filled cavity parallel to a rigid plane reflector at the other end, standing ultrasonic waves can be generated. Variations in the cavity length resulting from transducer motion lead to the generation of resonant frequencies lower than the drive frequency (known as fractional harmonics). The system was modeled by using a modified Mathieus equation whose solution resulted in the prediction of critical threshold drive amplitude for the excitation of parametric oscillation. The apparatus used by Adler and Breazeale was recently refined for accurate measurements of the threshold amplitude for parametric excitation at frequencies ranging from 2 to 7 MHz. The measurements showed that in this range the threshold amplitude increases with increasing drive frequency in apparent discrepancy with the results of Adler and Breazeale. Analysis of the theory indicates, however, that both past and current results lie in two different stability zones, and each is in agreement with the existing theory.