An efficient approach to computing third- order scattering of sound by sound with application to parametric arrays

A mathematical description of third-order scattered sound fields is derived using a multi-Gaussian beam (MGB) model that describes the sound field of any arbitrary axially symmetric beam as a series of Gaussian base functions. The third-order intermodulation (IM3) frequency components are produced by considering the cascaded nonlinear second-order effects when analyzing the interaction between the first-and second-order frequency components during the nonlinear scattering of sound by sound from two noncollinear ultrasonic baffled piston sources. The theory is extended to the modeling of the sound beams generated by parametric transducer arrays, showing that the MGB model can be efficiently used to calculate both the second- and third-order sound fields of the array. Measurements are presented for the IM3 frequency components and parametric array sound fields and comparisons of the model are made with traditional simulation results from direct numerical integration.