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In this paper, the partial-wave expansion method is applied to describe thedifference-frequency pressure generated in a nonlinear scattering of twoacoustic waves with an arbitrary wavefront by means of a rigid sphere.Particularly, the difference-frequency generation is analyzed in the nonlinearscattering with a spherical scatterer involving two intersecting plane waves inthe following configurations: collinear, crossing at right angles, andcounter-propagating. For the sake simplicity, the plane waves are assumed to bespatially located in a spherical region which diameter is smaller than thedifference-frequency wavelength. Such arrangements can be experimentallyaccomplished in vibro-acoustography and nonlinear acoustic tomographytechniques. It turns out to be that when the sphere radius is of the order ofthe primary wavelengths, and the downshift ratio (i.e. the ratio between thefundamental frequency and the difference-frequency) is larger than five,difference-frequency generation is mostly due to a nonlinear interactionbetween the primary scattered waves. The exception to this is the collinearscattering for which the nonlinear interaction of the primary incident waves isalso relevant. In addition, the difference-frequency scattered pressure in allscattering configurations decays as $r^{-1} \ln r$ and $1/r$, whereas $r$ isthe radial distance from the scatterer to the observation point.

Difference-frequency generation in nonlinear scattering of acoustic waves by a rigid sphere