Nonlinear acoustics in the presence of an object with sum or difference frequency sensing

Abstract

A general and complete second-order theory of nonlinear acoustics in the presence of an object is derived and shown to be consistent with experimental measurements. The total second-order field occurs at sum or difference frequencies of the primary fields and naturally breaks into (A) nonlinear waves generated by wave-wave interactions, and (B) second-order scattered waves that include the effect of centriodal motion of the object driven by a complete second-order wave-exciting force. Analytic expressions for second-order fields due to combinations of planar and spherical wave-wave interactions are derived. Wave-wave interactions are analytically shown to always dominate the total second-order field at sufficiently large range and carry only primary frequency response information about the object. As range decreases, the dominant mechanism is shown to vary with object size, boundary condition, and frequencies making it sometimes possible for sum or difference frequency response information about the object to be measured from second-order fields. Unique opportunities arise for nonlinear sum or difference frequency sensing that differ substantially from traditional sensing by linear scattering. Analytic proof shows that there is no scattering of sound by sound outside the region of compact support intersection of finite-duration plane waves at sum or difference frequencies, to second-order.