ABSTRACT
It is the task of this chapter to lay the theoretical foundations of the remainder of the book. Our emphasis is placed on relating measurable acoustic quantities, principally the speed and absorption of sound, to thermophysical properties of the medium. It is theory of that kind that allows acoustic measurements to serve as a tool in the study of thermodynamic and transport properties of gases and liquids. We shall devote most of our attention in this chapter to theory in which the medium is regarded as a classical continuum fluid. The results of this treatment will be applicable at frequencies small compared with those of molecular collisions or, in other terms, for wavelengths large compared with the mean free path. From the perspective of thermophysical property measurement this places few constraints upon the application of acoustic techniques; in practice, the only important effects arising from the finite length of the mean free path occur for dilute gases in the boundary layers near to an interface. Such small effects may be treated with sufficient accuracy by very simple kinetic theory. Molecular energy transfer and other relaxation mechanisms can be of much greater importance because they may be characterized by relaxation times orders of magnitude greater than the time between binary collisions. Here we include in our treatment of dissipation a bulk viscosity that arises from relaxation mechanisms other than the classical viscothermal processes, but we delay to a later chapter discussion both of the mechanisms themselves and of their consequences at frequencies that are not small compared with the inverse of the relevant relaxation time. Of course dynamic effects at high frequencies are of great interest in themselves. Attempts to explain the propagation of sound in rarefied gases at frequencies comparable with the molecular collision frequency touch on fundamental limitations within our present kinetic theory, while evaluation of the bulk viscosity from molecular properties presents severe difficulties. However, these are effects beyond the scope of this chapter.
