Theory and three-dimensional numerical simulation of sound propagation along a long enclosure with side opening

The sound properties along a long rectangular enclosure with a circular source on the top wall and rectangular opening at the side wall are studied. A mathematical model of average pressure at an opening contributed by the sound source and assuming air piston at the opening is derived in terms of the acoustic mode for a rigid duct. Three-dimensional numerical modelling is conducted to compare the theoretical prediction. The computational domain of interest is a long rectangular block associated with an opening connected to a free field environment. Non-reflecting portion is applied to each end of the domain. Sound pressure variations of discrete propagating mode are investigated. Interactions between the resonance of closed duct and effect of the opening are demonstrated at various frequencies. Comparisons indicate that the theoretical predictions give consistent results with that of numerical models. Precision of the radiation impedance of aperture is found crucial to the accuracy of mathematical model. This study approach including the theory and simulation provides a constructive framework for further examination of related subjects.