Abstract
We study acoustic waves propagating in two-dimensional (2D) systems consisting of steel cylinders surrounded by air. We use the plane-wave method in order to get the band structure of waves propagating in an infinite periodic system. In addition, we employed, for the first time for acoustic waves, the transfer matrix method in order to find the transmission coefficient of waves propagating along a system with a finite thickness. Both methods are in good agreement with each other and their results agree with recent measurements in a similar system (R. Martinez-Sala et al., Nature, 378 (1995) 241). We also find the optimum conditions for the appearance of spectral gaps.