Acoustic Radiation Pressure of Plane Compressional Waves

Both electromagnetic and acoustic waves exert forces of radiation upon an obstacle placed in the path of the wave, the forces being proportional to the mean energy density of the wave motion. In electromagnetics the action of these forces is relatively easily understood through the concept of Maxwell's electromagnetic stress tensor.The physical processes leading to these forces in a sound wave have been found to be considerably more complex; the difficulties belong to the fact that the acoustic wave equation is not linear and that a beam of finite cross section is subject to effects caused by the surrounding medium.Though many papers have been devoted to the subject and though various theoretical approaches have been made, some difficulties still seem to stand in the way of a clear understanding of the physics of the problem.The purpose of the present study is especially to throw light on the physical aspects. The approach adopted, which uses the momentum theorem, is believed to serve this purpose especially well. The expression for the radiation pressure is given in both Eulerian and Lagrangian coordinate systems.Special consideration is given to liquids of constant compressibility, since in such media the processes involved can be dealt with mathematically in a simple manner. The general case of a plane reflector with arbitrary reflection coefficient is treated; the modus operandi of the forces at the interface between liquid and obstacle is explained for some special cases, including the radiation forces on the interface between two nonmiscible liquids.Finally, a general relation is established between the energy density and the pressure caused by radiation falling normally upon a plane reflector, which, under certain assumptions, is valid in any fluid and at any amplitude.