Analytical relationship between sound relaxational absorption and sound speed dispersion in excitable gases

Whether sound relaxational absorption and sound speed dispersion can be used as two independent acoustic parameters for gas sensing or not is still uncertain. In this paper, the analytical relationship between the frequency-dependent sound relaxational absorption and sound speed dispersion in excitable gases is derived and analyzed. First, the coefficient of compressibility in the Newton–Laplace equation of sound speed is extended to an effective one for relaxing gas. Second, using the relationship between the effective coefficient of compressibility and the effective wave number, we obtain the analytical relationship between sound relaxational absorption and sound speed dispersion from the high-frequency and the low-frequency sound speeds, respectively. The derivation and the simulation results for gas mixtures, including carbon dioxide, methane, and nitrogen, demonstrate that the ratio of the high-frequency sound speed to the low-frequency sound speed determines the amplitude of acoustic relaxation absorption peak, that the inflection frequency of sound speed dispersion is consistent with the relaxation frequency of sound relaxational absorption, and that sound speed dispersion contains all molecular information carried by sound relaxational absorption and is more applicable to acquiring the molecular geometry, the vibration frequency, and other gas molecular characteristics. This paper provides a more theoretical basis on using acoustic speed dispersion for gas sensing.