The existence of full gaps and deaf bands in two-dimensional sonic crystals

Theoretical and experimental determination of sonic band structures of two- dimensional (2-D) arrays of rigid cylinders in air is reported. We present measurements for square and triangular lattices. A variational method is em ployed to Calculate the acoustic dispersion relation. Experimentally, a tra nsmission technique and the analysis of the phase delay between the inciden t and scattered waves by the structure are used to construct the acoustic b ands. The comparison between theory and experiments allows to fully charact erize the band gaps and it has also demonstrated the existence of deaf hand s; i.e., bands which cannot be excited due to symmetry reasons. For the cas e of square lattice we show that the structure with a filling fraction of 0 .41 has a full acoustic gap.