Empirical formulas for the prediction of the diffraction field around rigid, absorbing, single or multiple wedges

Abstract

The diffraction field around infinitely long wedges is investigated. Empirical formulas are derived based on a recently published approximate analytical diffraction solution. Empirical formulas reduce drastically the time required for the evaluation of the diffracted field compared to analytical solutions. Empirical formulas can, therefore, be of practical interest in cases of complex geometries with many diffracting edges. Compared to existing empirical formulas they provide increased accuracy, greater computational speed, and a wider range of applicability. Specifically, unlike existing empirical formulas, the proposed formulas can be applied: (i) to all wedge angles, (ii) to all receiver locations, and (iii) for all three types of simple sound sources: plane wave sources, line sources or point sources, both omni-directional and directional. Furthermore, they can be applied to low frequencies, a characteristic that is unique to the best of the authors’ knowledge. For low frequencies, their validity is limited to the cases where the distances of the source and the receiver from the edge differ by at least one order of magnitude. The suggested empirical formulas are incorporated into appropriate analytical models and can be applied to absorbing wedges and to diffraction by multiple wedges. Finally, good agreement is shown with published experimental data and numerical results for: (i) rigid or absorbing wedges, (ii) multiple rigid wedges, (iii) multiple absorbing wedges, and (iv) wedges with mixed surfaces (rigid /absorbing).