Parametric Scaling Laws. Part I. An Analytical Model for Predicting the Saturation Limits of a Parametric Array
Final rept. 1 Feb-31 Jul 1974
WESTINGHOUSE RESEARCH AND DEVELOPMENT CENTER PITTSBURGH PA
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Following a review of the approximate models previously used to provide parametric scaling laws, an exact solution for the asymptotic far-field pressure of a parametric array is derived from the plane wave form of Burgers equation. The influence of spherical spreading losses is then included by matching the solution at low primary wave amplitudes with a spherical wave solution obtained by the method of successive approximation. From the matched asymptotic solution, the referred pressure of the difference-frequency signal at one meter from the source i.e., the equivalent difference-frequency source level is derived as a universal function of scaled primary wave amplitudes, frequencies, source dimensions, and physical constants of the medium. With the aid, this function, which defines the saturation limit for a parametric array, the maximum conversion efficiency can be evaluated for a particular set of input parameters.
- Industrial Chemistry and Chemical Processing