Analytical and numerical solutions of the ‘‘General Theory Scattering for the Scattering of Sound by Sound’’ in several useful limits

Integral equations which form the basis of ‘‘A General Theory for the Scattering of Sound by Sound’’ [H. C. Woodsum and P. J. Westervelt, J. Sound Vib. 76(2), 179–186 (1981)] have been solved in several useful limits. In the case of the parametric array, the theory is shown to reduce in the appropriate limit to the models of Blue as well as Berktay and Leahy, as corrected by Mellen and Moffett [J. Acoust. Soc. Am. 60, 581–583 (1976)]. In the case of intersecting sound beams, the theory is shown to agree with predictions by Westervelt, as well as recent experimental results on the nonscattering of sound by sound [R. Roy and J. Wu, in Proceedings of the 13th International Symposium on Nonlinear Acoustics, edited by H. Hobæk (Elsevier Science, London, 1993)]. A by‐product of the theory is a useful parametric array model for arbitrary primary field geometries; numerical results are presented which are compared to the computer model of Mellen and Moffett.