Amplitude reflections and interaction solutions of linear and nonlinear acoustic waves with hard and soft boundaries

Abstract

In this study, the propagation of a fundamental plane mode in a bifurcated waveguide structure with soft–hard boundaries is analyzed by using the Helmholtz equation. The explicit solution is given to this bifurcated spaced waveguide problem by means of matching the potential across the boundary of continuity. Amplitudes of the reflected field in all those regions have been evaluated, and the energy balance has been derived. We have observed the reflection of the acoustic wave against the wavenumber and shown its variation with the duct width. Convergence of the problem has been shown graphically. In our analysis, we notice that the reflected amplitude decreases as the duct spacing increases; as a result, the acoustic energy will increase as the duct spacing increases. It is expected that our analysis could be helpful to give better understanding of wave reflection in an exhaust duct system. We then reduce the linear acoustic wave equation to the Kadomtsev–Petviashvili (KP) equation. Multiple-periodic wave interaction solutions of the KP nonlinear wave equation are investigated, and the energy transfer mechanism between the primary and higher harmonics is explained, which, to the best of our knowledge, is overlooked.