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Abstract

Propagating waves represent an aspect of more general forms of motion that can be described by the exact equation of continuum mechanics. Although a study of general forms of motion is practically possible only by means of numerical methods, their wave aspects can be expressed in terms of an elementary theory. The basic concepts of such a theory were established as a generalization of experimental facts long before mechanics itself appeared as a branch of mathematical physics. Only much later were they derived as consequences of the exact equations of mechanics. This system of concepts has an important property — it allows us to build a simple wave-propagation theory common to waves of any kind. That is why the basic concepts of wave-propagation theory can be introduced by considering the simplest equation of motion and then generalizing to more complex situations. Here we consider these concepts in the case of the scalar wave equation where f* and F* are functions of space coordinates (x1, x2, x3) and time t and c is a function of space coordinates only.

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