A New Approach to Definition of the Energy Density of Plane Acoustic Waves

摘要

It is known that, in a plane acoustic wave, the instantaneous total energy density calculated by the classical method [1] is a function of the time and is not the integral of motion [2]. For plane homogeneous waves (bulk acoustic waves, BAWs), the instantaneous densities of the potential and kinetic energy are always equal to each other at any point of a medium; that is, the densities of these energies change in phase [1]. This means that, in this case, the transformation of potential energy into kinetic energy and vice versa, which is typical of oscillatory processes, is absent. For plane inhomoge-neous waves (surface acoustic waves (SAWs) and waves in plates), the instantaneous energy density at a fixed point of a medium is not very informative, since the time-average densities of potential and kinetic energies are not equal to each other [2]. Certain regularities begin to manifest themselves when we integrate the energy density along the normal to the interface and consider the time-average wave energy per unit aperture. However, the aforementioned features are not mandatory in the case of propagating mechanical waves. For example, for gravitational waves on the surface of a liquid, the total energy density at any point of the liquid is the integral of motion and does not depend on the time [3]. In this case, the potential energy transforms into kinetic energy and vice versa, provided that these processes are considered separately along the direction of wave propagation and along the normal to the surface of the undisturbed liquid.