In recent years, the study of metamaterials based on periodic structures such as sonic crystals has been gaining importance. However, their study depends on laboratory conditions that are impossible to achieve in practice. Therefore, the use of numerical simulations is required to study the sound propagation within these structures.

In order to achieve an adequate depth of study, it is necessary to study the performance of this type of barriers at any incidence angle of an acoustic wave. In order to reduce the computational cost of the simulations, different approaches have been developed to implement periodic boundary conditions that simulate an infinite domain in which waves can propagate at a specific angle of incidence.

In this work, different methods applied to the acoustic analysis of metamaterials will be studied using the finite difference method (FDTD). Their suitability, the accuracy of their results and the parameters necessary for their correct performance will be compared in order to obtain the parameters that define the real behaviour of a sonic crystal.