Low-Frequency Propagation of Plane Scalar Waves through a Periodic Array of Arbitrary Volumetric Obstacles

In the context of wave propagation through gratings of periodically distributed obstacles, we use analytical approaches to derive explicit formulas for scattering parameters in the low-frequency approximation. The geometric shape of the obstacles is arbitrary. The numerical solution of the main integral equations for assigned shapes provides some graphs, and a comparison with previous results shows that some of these are incorrect or hold under very restrictive conditions.