Preston Smith's theory of the effect of heat radiation on sound propagation in gases

Abstract

The 1996 Trent-Crede Medal encomium by Barger states that Smith's favorite paper was "Effect of heat radiation on sound propagation in gases" (JASA, 1957). Smith stated this also in a private communication some time earlier to the present writer. The paper was prompted by works by Stokes and Rayleigh in which heat effects were modeled by Newton's law of cooling, which presumes that the heat radiation out from a limited region of heated matter is proportional to the difference of the local temperature and that of the surrounding medium. Stokes in 1851 constructed a theory for how this assumption leads to a prediction of the dependence of phase velocity and attenuation on frequency, and this theory was used by Rayleigh in the Theory of Sound to analyze whether acoustical fluctuations were more nearly isothermal or adiabatic. However, as Smith pointed out, apparently for the first time, neither Stokes and Rayleigh fully understood the relevant physics. When the atomic nature of heat radiation within gases is taken into account, the effect of heat radiation (in contrast to the effect of thermal conduction) is negligible at all frequencies. For all frequencies for which the attenuation is small, the acoustic fluctuations are adiabatic.