Scattering of Sound by Sound from Gaussian Beams and Parametric Reception Near a Reflecting Surface.

A quasilinear solution of the Khokhlov-Zabolotskaya -Kuznetsov equation is derived for the case of two Gaussian beams that intersect at a small angle. In the absence of absorption, a closed-form solution is obtained which is a generalization of the result obtained for parametric receiving arrays by Hamilton, Naze Tjotta, and Tjotta (J. Acoust. Soc. Am. 82, 311-318 (1987)). The solution is used to investigate two problems, (1) the scattering of sound by sound, and (2) the ability of a parametric receiving array to discriminate against multipath interference. In the first investigation, significant levels of scattered sum and difference frequency sound are shown to exist outside the interaction region that is formed by two intersecting primary beams. An asymptotic formula reveals that sum or difference frequency sound is scattered in the approximate direction of k _1+/- k_2, where k_{j} is the wave vector associated with the direction and frequency of the j th primary beam. Computed propagation curves and beam patterns demonstrate the dependence of the scattered radiation on source separation, frequency ratio, and interaction angle. No scattered sound is observed when the axes of the two primary beams cross in the farfield. The results are in good agreement with those of Berntsen, Naze Tjotta, and Tjotta (accepted for publication in J. Acoust. Soc. Am.), which are valid for arbitrary interaction angles and amplitude distributions. Effects of absorption and focusing are also considered. In the second investigation, solutions for the scattering of sound by sound are combined using the method of images to study the ability of a parametric receiving array to measure the freefield directivity of a source in the neighborhood of a reflector. Consideration is given primarily to directive underwater sources whose acoustic axes are parallel to the air-water interface. The pump is located on the source and radiates a directive high intensity beam through the sound field. Cases are shown for which the difference frequency sound detected by a hydrophone on the axis of the pump beam provides reasonable freefield source directivities in the presence of multipath components.