Interaction of sound waves. Part II: Plane wave and real beam

Abstract

The nonlinear interaction in a lossless fluid between an infinite plane sound wave and a sound beam generated by a real source is considered theoretically in the quasilinear approximation. The importance of a proper choice of acoustic variables and their correct on‐source values are analyzed. The governing equation for the sum and difference frequency components is solved for prescribed boundary conditions. A solution uniformly valid in space is obtained in the form of a double Fourier integral. In the farfield, the integration can be performed and a simple formula is obtained. This relates the amplitude and directivity at the observation point to the on‐source amplitude and phase of the beam. Relevance to earlier literature on parametric acoustic receiving arrays is also discussed.