Analytical model and numerical simulation of internal sound fields of an infinitely long duct with aperture array

The sound leaking behavior along an infinitely long rectangular duct with multiple rectangular apertures at the side wall are investigated in the present study. Each aperture is modelled as an vibrating air piston. Based on the theory of average acoustic pressure at an aperture contributed by the sound source and mutual contributions by other apertures for a rigid duct, sound pressure variations of discrete propagating modes are determined analytically. Numerical simulation is generated in three-dimensional form to compare with the results of analytical prediction. A long block with multiple apertures connected to free field is treated as the interested domain. Both ends of the domain are fixed by non-reflecting portion. Comparisons show that the leaky sound predictions of analytical model are in line with the numerical results. The width variation of the hard wall between apertures, namely fin, is found to have influence on the accuracy of the analytical prediction. This study indicates significance of possible sound diffraction by the apertures under the action of sound excitation.