Sound isolation from cubic arrays of air bubbles in water

Abstract

We present systematic and extensive evidence for the existence of complete, multiple, huge stop bands in the band structure for cubic arrays of air bubbles in water. We investigate face-centered cubic (fcc), body-centered cubic (bcc), and simple-cubic (sc) arrangements using the Fourier series expansion method which does not require matching of the messy boundary conditions. The lowest stop bands are largest for a volume fraction f ≤ 10%, with a gap/midgap ratio of ≈ 1.8 for all the three geometries. Surprisingly interesting but rigorously justifiable is the fact that the low-frequency flat passbands for the perfectly periodic systems correspond to the discrete modes of a single bubble. This is an antifact of the low filling fraction and huge density contrast in air and water. We stress that such a simple inhomogeneous system as made up of air bubbles in water exhibits the widest stop bands ever reported for elastic/acoustic as well as dielectric composites.