On sound propagation along an infinite rectangular duct-like structure with a finite slot opening and its modelling

The sound propagation across a sound leaking section along an infinite rectangular duct-like structure near to the lower order duct eigenfrequencies is investigated numerically in the present study. The sound leakage is achieved by finite length rectangular slots located at a corner of the duct-like structure cross section. The finite-element simulations are performed, in the first place, to gain insights into the modal development inside the structure. A semi-analytical model, which considers the wavy air motions along the slots with oblique sound radiation patterns, is developed. An empirical framework is also proposed to estimate the complex longitudinal wavenumber along the slot using the numerical results and dimensional analysis. The performance of the proposed semi-analytical model, together with the complex wavenumber prediction framework, is tested using two duct-like structures with different cross section aspect ratios. The results show that the present proposed approach gives predictions close to the finite-element simulations. The deviations are well within engineering tolerance.