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The acoustical properties of sound in a long rectangular partial enclosure with various opening sizes and positions are investigated numerically in the present study. The finite element method is adopted to estimate the mode shapes across the cross section of the partial enclosure inside a free field environment. Some acoustic modes with patterns similar to some of the rigid-wall duct modes are found. The sound propagates in form of modes inside the partial enclosures as in the rigid-wall duct case. The long partial enclosure leaks sound and the opening radiates sound into a free space in the numerical model. The sound radiation is associated with the interactions between acoustic mode shape of the partial enclosure, opening size and position. Results indicate that the behaviour of acoustic pressure radiated from the opening is a significant effect on the resonance frequencies.

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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.