Transport theory of ultrasonic attenuation

Abstract

AbstractThe transport theory of ultrasonic attenuation is critically examined. The Pippard expression for arbitrary band structure is derived from the traditional transport approach without introducing Pippard's fictitious forces. The validity of using the relaxation‐time approximation in the transport equation is investigated, and the analysis is extended beyond this approximation. It is pointed out that for the general collision integral the relaxation time appearing in Pippard's theory may have an imaginary part. Pippard's expression for the attenuation is shown to be valid only when the relaxation time is real, and this will occur when the mean‐free path is either much less or much greater than the wavelength of sound, and in the case of “quasi‐catastrophic” scattering. Finally, some inconsistencies in the literature are pointed out.