Scientia Sinica

38 g SCIENTIA SINICA Vol, V

The fact that equation (15) may be derived from equation (4) suggests that Liebermann’s equation for sound absorption due to chemical relaxation may also be obtained directly from the result of our visco-elastic theory. This will be shown in § V.

Thus, our visco-elastic theory is seen to include all three. mechanisms. Thermal relaxation is expected to exist in the case of polyatomic gases and possibly in certain gas-like organic liquids. Structural relaxation can only occur with liquids. Chemical relaxation may exist in gas mixtures and solutions. Of course, either because more than one relaxation times may be present for a single relaxation mechanism or because two or all three kinds of relaxational mechanisms referred to above may exist simultaneously, the multi-relaxational visco-elastic theory given in reference [3] may be needed.

Since all the three relaxations are phenomenologically equivalent, it is. necessary to rely on molecular theories for their identification. It seems that there exists but one convincing type of calculations leading to this identification, viz., when the energy levels of the various modes of vibrations of the molecules have been found from spectrum analysis, C“” may be calculated by statistical mechanics and the identification with the thermal mechanism may be made by calculating sound absorption or dispersion with it by means of KneserBourgin formula. Furthermore, the temperature dependence of absorption coefficient is different for different mechanisms, and although much remains to be studied regarding the details of these relations it seems that their qualitative indications have promised to serve as a possible aid for deciding the correct mechanism (see Markham e al'"*!, pp. 379—398).

III. Derivation oF Kneser-Bourcin Equations oF SounD

ABSORPTION FROM VOLUME VIsco-ELASTIC THEORY

Confined to the case of a single relaxation time 7, for a pure gas or a gas-like liquid, equation (7) or (8) gives for the sound absorption coefficient per wave length due to volume viscosity (see equation (24) of reference [2], being denoted there by y2)

_>,— Prem _, Bw B= 28 BE Ba wth" TEP) Bow?” (16)

whose maximum value occurs at the frequency

Ue 1 Bo Uo T2 T2 Ba ~

(17)

Om =

_ In terms of o,, (16) takes the form