A statistical theory for sound radiation and reflection from a duct

A new analytical method is introduced for the study of the sound radiation and reflection from the open end of a duct. The sound is thought of as an aggregation of the quasiparticles-phonons. The motion of the latter is described in terms of the statistical distribution, which is derived from the classical wave theory. The results are in good agreement with the solutions obtained using the Wiener-Hopf technique when the latter is applicable, but the new method is simple and provides straightforward physical interpretation of the problem. Furthermore, it is applicable to a problem involving a duct in which modes are difficult to determine or cannot be defined at all, whereas the Wiener-Hopf technique is not.