Propagation of two-dimensional vibroacoustic disturbances in a rarefied gas

We study the effect of gas rarefaction on the propagation of vibroacoustic sound in a two-dimensional setup of a gas confined by a planar oscillating wall. Focusing on small-amplitude harmonic excitations imposed to only part of the surface, the problem is analyzed in the entire range of gas rarefaction rates, governed by the ratio between the gas mean free path and wavelength of a prescribed wall signal. Analytical solutions are obtained in the free-molecular and continuum limits, consisting of the gas response to a delta function and other locally confined wall actuations. The analysis is supplemented by direct simulation Monte Carlo calculations in the intermediate range of gas rarefaction rates. Remarkably, distinct differences are observed between sound propagation characteristics in the two limits. At continuum-limit conditions, the acoustic signal propagates isotropically in a monopole-type pattern, and decays inversely to the square root distance from the source. In contrast, the signal in the collisionless flow regime is exponentially decaying away from the source and follows a “nearly dipole-type” directivity field, where the acoustic pressure vanishes in the direction normal to the source axis of motion. The differences in results, stemming from the fundamentally distinct continuum and ballistic flow models, are discussed and rationalized in terms of the analytical limit-case descriptions.