Essential role of impedance in the formation of acoustic band gaps

We investigate acoustic band gaps (ABGs) in a two-dimensional lattice of cylinders for the cases of constant impedance, Z, and constant velocity, $\mathrm{v.}$ ABGs become wider for the case of constant $v$ (varying $\mathrm{Z),}$ and become smaller, eventually disappearing in the opposite case. As the volume fraction increases, the upper (bottom) edge of the stop band increases (decreases) and then decreases (increases) in composites with impedance variation only, so that the midgap frequency changes very little and a larger ABG can be created. The upper (bottom) edge of the stop band increases (decreases) when the impedance ratio increases, so that the midgap frequency decreases slightly and the size of the ABG increases.