Acoustic radiation pressure in a three-dimensional lossy medium

Acoustic radiation pressure exerted by an arbitrary acoustic wave in a three-dimensional lossy medium is calculated by extending an indirect approach developed by Chu and Apfel [B-T. Chu and R. E. Apfel, 'Acoustic radiation pressure produced by a beam of sound,' J. Acoust. Soc. Am. 72, 1673-1687 (1982)]. Without appealing to the detailed solutions of equations governing fluid motion, a general analytic expression for the radiation pressure in lossy media with arbitrary waves is obtained. When an infinite lossy medium is considered, the expression states that the radiation pressure, to the lowest order of approximation (i.e., second order), is equal to corresponding total energy density. For a special class of confined spaces, the expression leads to a rather general formula for the radiation pressure, in which the radiation pressure is given in terms of various energy densities in the field. Furthermore, a relationship among these energy densities is generalized to the case of lossy media, which enables one to compute the radiation pressure in the class of spaces with the knowledge of the first-order perturbation solution only.