Total acoustic transmission between fluids using a solid material with emphasis on the air-water interface

Abstract

Total acoustic transmission between water and air is modeled using a purely solid interface comprising two elastic plates separated by periodically spaced ribs. The frequency of full transmission depends only on, and is inversely proportional to, the areal density of the plate facing the air. Total transmission also requires a specific dependence of the rib spacing on the bending stiffness of the two plates. These relations are the result of an explicit analytical solution for the transmitted and reflected acoustic waves combined with asymptotic approximations based on the small parameter defined by the air-to-water impedance ratio. Surprisingly, the total transmission effect is almost independent of the angle of incidence, even though the transmission conditions are predicated on normal incidence. Parametric studies are performed to examine the effect on the frequency bandwidth and Q-factor of the acoustic transmissivity. A lower bound for the Q-factor of $30.6$ is simply related to the water-air impedance ratio.