Interaction of sound waves. Part IV: Scattering of sound by sound

Abstract

A theory for the nonlinear interaction between two sound beams produced by real sources in a lossless fluid was presented in a previous work [Naze Tjo/tta and Tjo/tta, J. Acoust. Soc. Am. 83, 487–495 (1988)]. A general solution of the governing equation in the quasilinear approximation, valid at any range, crossing angle, and frequency ratio, was obtained for prescribed boundary conditions. An asymptotic formula for the sum and difference frequency sound pressure was obtained at large distance from the sources. It relates the amplitude and directivity of the sound field in the farfield to the on-source conditions. In the present work, the theory is further developed, and numerical results are presented for uniform piston and Gaussian sources. The influence of source geometry (separation, and intersection angles from 0° to 90°) and frequency on the beam pattern of the nonlinearly generated sound is studied. The results obtained are related to earlier works on scattering of sound by sound, which are discussed. Necessary conditions are also given to determine when scattering of sound by sound can be observed. In the special case of thin Gaussian beams intersecting at a small angle, the results are compared with that obtained by Darvennes and Hamilton [submitted to J. Acoust. Soc. Am.] using the paraxial approximation. Also discussed are some properties of the automatic global adaptive quadrature routine used to compute the two-dimensional integral in the asymptotic formula.