Experimental and theoretical investigations of dispersion of ultrasonic waves in the low-temperature and low-pressure nitrogen gas

Abstract

Temperature has a complex effect on acoustic dispersion in dilute gases. In this paper, the effect of temperature on the acoustic dispersion of dilute gases is analyzed theoretically and experimentally. Theoretically, the Navier–Stokes (NS) equation and the Greenspan's theory, which includes the rotational-relaxation correction, are applied to calculate the dispersive sound speed. It is concluded that the temperature affects the molecular translational relaxation and the rotational relaxation by influencing the average molecular collision frequency and the relaxation collision number, respectively, and thus, change the amplitude of the acoustic dispersion. Numerical calculations led to the conclusion that both translational and rotational dispersions weakened as the temperature decreased. Experimentally, sound speed measurements of 21–40 kHz acoustic waves were also carried out in gaseous nitrogen at temperatures ranging from −70 °C to 20 °C and pressures of 150–105 Pa. Theoretical predications indicate that the speed of sound should increase with decreasing pressure at all temperatures, and the degree of dispersion should diminish at lower temperatures. The experimental observation of dispersion is consistent with theory within experimental error (1%) but was not able to distinguish the small (0.01%) increase in sound speed expected at 150 Pa.