An Extension to the Directive Line Source Model for Diffraction by Half Planes and Wedges

The present work enhances the Directive Line Source Model (DLSM), one of the models that predict the diffraction field produced by a sound wave incident on a half plane, to render it valid close to the shadow boundaries, where it was not valid before. It is shown that the diffraction field can be interpreted as radiation from a directional line source (as stipulated by the original DLSM) irrespective of the receiver proximity to a shadow boundary, provided that the directivity of the virtual line source is appropriately modified. The new directivity function is investigated, its parameters recast and appropriate simpler asymptotic forms presented. Further, based on the new directivity function and in accordance with the changing nature of the diffracted signal, a new, precisely defined separation of the diffraction field around the shadow boundaries is proposed, which also provides a computational advantage for large scale simulations. Finally, the proposed reformulation of the diffraction solution and of its parameters enables the application of the model to three cases of practical interest: (i) directional sound sources, (ii) diffraction by edges of finite length, and (iii) diffraction by wedges, where the proposed formulation is considerably faster to compute than the well-established solution. In all cases, predictions compare favorably with laboratory measurements and/or other analytical solutions.