Study of various periodic acoustic lattices by two methods: Transfer matrix and Green's method

The objective of this study is to analyse two kinds of periodic infinite lattices widely used in acoustic filtering. The first network is formed by periodic close resonators and the second by periodic open resonators. Then we realize a combination of these two systems and we study and compare the effect on the band gap. Resonators are filters often used to reduce noise. We calculate the dispersion relation theoretically and numerically in this paper by using the matrix transfer method. Then, the results obtained are compared with those of the Green's function method often used in solid state physics.