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

Abstract

The sound propagation across a sound-leaking section along an infinite rectangular duct-like structure near to the lower order duct eigen-frequencies is investigated numerically in the present study. The sound leakage is achieved by finite length rectangular slots located at a corner of the ductlike structure cross section. Finite-element simulations are carried out 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 wave number along the slot using the numerical results and dimensional analysis. The performance of the proposed semianalytical model together with the complex wave number prediction framework is tested using two duct-like structures with different cross section aspect ratios. Results show that the present proposed approach gives predictions close to finite-element simulations. The deviations are well within engineering tolerance.