Acoustic radiation pressure

Abstract

Several apparently contradictory definitions for radiation pressure are in current use, and a number of authors have commented on the confusion which exists. This paper develops a unified and simple treatment of the subject, correct to all orders of approximation, in which radiation pressure appears as a true field parameter. It is shown that the definition of radiation pressure proposed here can be reconciled with most of the current definitions and that much of the apparent contradiction is illusory. It is indicated that, in the absence of attenuation, the force on an obstacle in the field can be related exactly to two field quantities, the time-averaged Lagrangian pressure, or, equivalently, the time-averaged momentum flux, without any assumption as to the equation of state of the medium. It is explained, however, that the majority of authors prefer not to use one of these field quantities, but, instead, attempt to relate radiation pressure to another quantity such as energy density. In the second part of this paper, therefore, a derivation is given of the relation of radiation pressure, as defined, to the kinetic and potential energy densities to all orders of magnitude for a fluid obeying the Tait equation of state. The second order approximation to this relation is compared with the results of other writers and some discrepancies in published values are resolved.