Parametric receiving array and the scattering of sound by sound

The scattering of interaction-frequency components from two sound waves interacting at a nonzero angle has been the subject of controversy for the last two decades. This paper attempts to provide better understanding of the problem by discussing the relationship found between the scattering of sound by sound and the parametric receiving array. First, the solution for a high-frequency plane wave interacting with a low-frequency plane wave over a half space is discussed. The high-frequency sound wave is assumed to originate at a planar boundary and to propagate away from it. Then the interaction-frequency components at some distance from this planar boundary are found. When this solution is related to a solution for a parametric receiving array with a low-frequency plane signal wave and a high-frequency narrowbeam pump wave, the two solutions are found to have very similar properties. Some experiments, as well as solutions, for various configurations of the parametric receiving array are discussed in light of the problem of scattering of sound by sound. Finally, some of the foibles associated with measurements of two interacting waves are described with the aid of the theoretical model for the parametric receiving array. In this paper interaction components are found to exist even when the two sound waves do not propagate in the same direction. It will also be shown that points exist along the nulls of the pump beam patterns where the one primary sound wave is zero and the interaction components are nonzero.