Heat Conduction Effects in Sound Emission

Abstract

This paper presents the mathematical formulation of the heat conduction phenomena occurring at the surface of a sound emitter, wherein the medium considered to be receiving the sound and impeding the motions of the source is a gas. The method employed is that previously used by Herzfeld to discuss reflection. The result is that due to the rapid, approximately adiabatic, compressions and rarefactions, an alternating temperature gradient and therefore temperature wave, is set up in the solid source and in the medium in such a manner as to cause a reduction in the total amount of sound energy radiated from the source. This effect is expressed in terms of two out-of-phase components of particle velocity amplitude. One is of the regular sound propagation, while one is a weak, slow, highly damped wave. The ratio of the regular wave amplitude to that of the source represents a complex coefficient of emission. This emission coefficient is compared with the reflection coefficient, and the losses are found to be just half as great as in the latter case. Such a complex emission coefficient implies the same form for the effective impedance of the medium on the source, i.e., the ratio of pressure to velocity, and accordingly this radiation impedance is partially reactive and partially resistive; each of these parts is given its explicit expression in terms of measurable physical characteristics of the medium. The results had previously been applied in the revision of Hubbard’s theory of the ultrasonic interferometer to take account of these heat conduction effects, and the experimental verification of the predicted reflection coefficients for several gases is taken as experimental justification of the theoretical synthesis given.