Interactions Between Elastic Waves in an Isotropic Solid

Interactions between elastic waves in an isotropic solid are studied in the elastic-continuum approximation. The analysis is carried out completely in a wave-packet formalism, i.e., scattering of wave packets by wave packets. The maximum amplitude (or intensity) and width of the scattered wave packet are expressed in terms of the maximum amplitudes, frequencies, widths, polarizations, and relative propagation directions of the primary-wave packets. The polarization relations and frequency ranges for the allowed interaction processes are obtained; these are essentially identical to the ones given by Jones and Kobett. The results are shown to be in good order-of-magnitude agreement with the experiments of Rollins. Possible application of elastic-wave scattering to the determination of third-order elastic constants is discussed.