A three-dimensional impedance transformer model for broadband acoustic transmission between water and air

Enhanced transmission of sound across the air-water interface is modeled with a system of three parallel elastic plates connected by periodically spaced columnar ribs. Maximum transmitted energy combined with optimal frequency bandwidth occurs when the central plate is far thicker than those facing air and water. This allows it to be replaced by a mass-like impedance, resulting in a simpler and accurate 2-plate model. Asymptotic analysis based upon the air-to-water impedance ratio, supported by simulations, provides explicit formulae for the system dimensions required for maximum broadband transmission.