Wave Propagation in an Ideal Gas: First and Second Sound

ABSTRACT

Propagation of sound waves through an ideal gas is studied in the framework of kinetic theory, starting from the integral representation of the Boltzmann Equation (BE). The distribution function is calculated and used to obtain the dispersion relation of density waves. The parallel existence of temperature waves (in some contexts referred to as second sound) is also part of this investigation. Temperature waves are found to exist; the phase difference between density and temperature waves is determined.

KEYWORDS:

• Integral form of the Boltzmann equation
• density waves
• temperature waves
• second sound

Acknowledgment

The third author graciously thanks the University of Bologna Institute for Advanced Study for hosting his stay during the completion of this work.