THE INITIAL-VALUE PROBLEMS IN ACOUSTICS, ELASTODYNAMICS AND ELECTROMAGNETICS

The initial-value problems for acoustic waves in fluids, elastic waves in solids and electromagnetic waves are discussed. The governing syst ems of first-order partial differential equations pertaining to arbitr arily inhomogenous and anisotropic media are taken as point of departu re and, correspondingly, the initial values of the pertaining two stat e quantities (i.e. the two quantities whose product specifies the area density of power flow in each of the wave motions) are prescribed. Th e initial-value problem thus posed is thought to be more physical (and turns out to be more complicated) than the conventional one associate d with the second-order wave equation in one of the two state quantiti es, where the inital values of this state quantity and its first-order time derivative are prescribed. For the cases of homogeneous, isotrop ic media, the initial-value problems are solved with the aid of a time Laplace and spatial Fourier transform method that bears resemblance t o the modified Cagniard method for solving transient wave propagation problems in layered media.