The rotational dispersion of sound in hydrogen

Abstract

The development of the interferometric method originally due to Pierce has definitely established the existence of an acoustic dispersion phenomenon in gases at supersonic frequencies. The experimental investigations of Abello, Kneser, Richards and Reid and others have shown this dispersion to exist in CO 2 , C 2 H 4 , CS 2 and SO 2 . An explanation of the mechanism of the effect was advanced by Rice and Herzfeld; and on the basis of this mechanism the dispersion formula has been derived by Kneser, Rutgers and Bourgin. The density variations produced in the gas by the sound wave result in a disturbance of the equilibrium distribution of energy between the various degrees of freedom of the molecule, there being excess of translational energy in the compressional phase for example. This equilibrium is then re-established, after a certain length of time which is characteristic of the gas, by inelastic collisions. When the period of the wave is of the order of this characteristic time, this exchange becomes incomplete and the specific heat of the gas diminishes, the sound velocity therefore increases until, as the frequency increases further, there is no time during a cycle for energy to be transferred. The sound velocity then approaches a constant value. In the case of all gases previously investigated it is quite certain that the dispersion is to be attributed to the failure of the vibrational energy exchanges to follow the acoustic cycle. However, recently Richards and Reid have reported certain effects which, they assert, indicate a dispersion region in hydrogen due to rotational energy lag and lying at least partly in frequency range 94—451 kc. However, on the basis of the classical kinetic theory of Jeans one would expect to find such a dispersion only at frequencies of the order 10 6 kc. Further, Richards states that the experimental accuracy in the case of the hydrogen measurements was not very great. For these reasons it was considered advisable to investigate this problem further.