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.

中文翻译：

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超声波在低温低压氮气中色散的实验与理论研究

温度对稀气体中的声学扩散具有复杂的影响。本文从理论上和实验上分析了温度对稀薄气体声扩散的影响。理论上，纳维-斯托克斯 (NS) 方程和格林斯潘理论（包括旋转弛豫校正）可用于计算色散声速。可以得出结论，温度分别通过影响平均分子碰撞频率和弛豫碰撞数来影响分子平移弛豫和旋转弛豫，从而改变声色散的幅度。数值计算得出的结论是，随着温度降低，平移和旋转色散都会减弱。实验上，⁵ Pa。理论预测表明，在所有温度下，声速都应随着压力的降低而增加，而色散程度在较低温度下应减小。色散的实验观察与实验误差 (1%) 内的理论一致，但无法区分 150 Pa 时预期的声速小幅增加 (0.01%)。