Low-Frequency Scattering by a Semi-Infinite Lattice of Cylinders

Acoustic wave scattering by a semi-infinite lattice of sound-soft cylinders is considered in the long-wave limit. The problem is first reduced to an infinite linear system of algebraic equations, and this in turn is solved via the discrete Wiener–Hopf technique. A complete description of the far-field is given, first for the case where there is no propagation through the lattice, and then for the situation in which Bloch waves are excited. Finally, we apply the principle of conservation of energy, which leads to useful identities that serve as a check on our results.