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Analytical methods are fundamental in studying acoustics problems. One of theimportant tools is the Wiener-Hopf method, which can be used to solve manycanonical problems with sharp transitions in boundary conditions on aplane/plate. However, there are some strict limitations to its use, usually theboundary conditions need to be imposed on parallel lines (after a suitablemapping). Such mappings exist for wedges with continuous boundaries, but fordiscrete boundaries, they have not yet been constructed. In our previousarticle, we have overcome this limitation and studied the diffraction ofacoustic waves by a wedge consisting of point scatterers. Here, the problem isgeneralised to an arbitrary number of periodic semi-infinite arrays witharbitrary orientations. This is done by constructing several coupled systems ofequations (one for every semi-infinite array) which are treated independently.The derived systems of equations are solved using the discrete Wiener-Hopftechnique and the resulting matrix equation is inverted using elementary matrixarithmetic. Of course, numerically this matrix needs to be truncated, but weare able to do so such that thousands of scatterers on every array are includedin the numerical results. Comparisons with other numerical methods areconsidered, and their strengths/weaknesses are highlighted.

Diffraction of acoustic waves by multiple semi-infinite arrays: a generalisation of the point scatterer wedge