General formulation of the dispersion equation in bounded visco-thermal fluid, and application to some simple geometries

Abstract

The purpose of this paper is to give a new set of equations derived from the basic classical theory of the acoustic propagation in visco-thermal fluid and valid in the time domain, and to provide us with a general dispersion equation for harmonic waves in several boundary problems of interest. It is shown that this dispersion equation generalizes some known results as the equivalent specific impedance of plane boundaries and resonance frequencies of spherical resonators, and that it provides us with a new general equation giving the propagation constant of waves for all kind of modes in rigid walled cylindrical tubes.