Sum and difference frequency generation in sound radiation from a vibrating planar boundary

Abstract

An earlier study [J. H. Ginsberg, J. Acoust. Soc. Am. 69, 60–65 (1981); 69, 929–936 (1981)] of sound radiation from a vibrating planar boundary considered the case of monochromatic excitation. That work featured perturbation analysis combining asymptotic integration and the renormalization version of the method of strained coordinates. The present analysis initiates an extension of those techniques to the case of a two‐frequency excitation. These frequencies are considered arbitrary; hence, the results for a parametric array (closely spaced frequencies) can be obtained as a special case of the present analysis. Using the Fourier transform in its conventional complex function form to describe the linearized signal leads to fomulation of the second‐order potential in terms of complex functions. A coordinate straining transformation describing the full spectrum (propagating and evanescent) is deduced. Accordingly, uniformly accurate expressions for the acoustic pressure and the velocity components are obtained.