Sound propagation at small scales under continuum and non-continuum transport

Using an observation by Lamb, namely that continuum sound wave propagation in sufficiently narrow channels is quasi-steady and isothermal, we obtain analytical predictions for the propagation of sound waves at small scales under non-continuum transport. We also extend Lamb's approach to include the effects of inertia and heat conduction for wave propagation at larger characterisitc scales descibed by continuum transport (no-slip and slip-flow regimes). Our theoretical predictions are compared to molecular-based direct Monte Carlo solutions of the Boltzmann equation. Very good agreement is found between theory and numerical solutions.