Model for parametric acoustic sources

Abstract

A theoretical model for the difference-frequency radiation from a parametric acoustic array is developed. The (two-frequency) primary wave is assumed to be radiated by a piston source and may be effectively limited in either the nearfield or the farfield of the piston. Either small-signal absorption or saturation of the primary beam may serve as the limiting mechanism. The parametric gain is defined as a complex number whose (i) magnitude is the ratio of secondary and primary source pressures and (ii) phase is an indication of how much generation occurs within the nearfield and how much within the farfield of the primary beam. The parametric gain is evaluated as a function of the primary-to-secondary frequency (downshift) ratio, the amount of small-signal primary absorption within the nearfield, and a ’’scaled’’ primary source level. Then, the parametric gain may be used to determine the beam pattern characteristics via a simple closed-form expression. The theoretical results are found to be in good agreement with other theoretical treatments (within their realms of applicability) and in fair agreement with experimental results from various types of parametric sources. The discrepancies that do exist appear to stem from the approximation that the primary nearfield can be treated as a plane wave.