Analysis of internally generated sound in continuous materials: (I) inhomogeneous acoustic wave equations

Abstract

Prior to the recent interest in aerodynamically generated sound, practically no attention had been given in acoustical work to radiation from volume distributions of sound sources, with the result that this subject is not discussed in any detail in acoustical literature or textbooks. This paper is the first of a series in which will be presented a critical, introductory account of the fundamental concepts and basic methods of analysis that are appropriate to these problems, and of multipole analysis in particular. To indicate that the methods can be applied to internally generated sound in materials other than fluids, it is shown in this first paper that the concepts of “aerodynamically generated” sound are applicable to any continuous material, provided that temperature, entropy and concentration (or progress variable) gradients are not too large. An inhomogeneous wave equation is derived, describing mass density fluctuations in a continuous material. Several different forms of this equation, and some aspects of the physical interpretation of these forms, are considered.