Scattering of sound by sound from two real beams

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 Tjøtta and Tjøtta, 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, numerical results are presented for various types of sources (uniform piston, Gaussian source, focusing source). The influence of source geometry (separation, and intersection angles from 0° and 90°) and frequency on the beam pattern of the nonlinearly generated sound is studied. 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 presented by Darvennes and Hamilton [J. Acoust. Soc. Am. Suppl. 1 83, S4 (1988)] using the paraxial approximation. [Work supported by the IR&D program of ARL:UT, and VISTA/STRATOIL, Norway.]