Interaction of sound waves. Part III: Two real beams

Abstract

This article is a theoretical study of the nonlinear interaction between two sound beams in a lossless fluid, intersecting each other at arbitrary angles. The governing equation for the sum and difference frequency components is solved in the quasilinear approximation for prescribed conditions on the sources of the two beams. A solution that is uniformly valid in space is obtained in the form of a Fourier integral. Asymptotic evaluations at large distance from the sources lead to simple formulas that relate the amplitude and phase of the generated sound to the on-source conditions. Diffraction effects are fully accounted for, and shown to be important even at large distances. Relevance to earlier literature on the scattering of sound by sound is discussed.