Coherent sound propagation across the effective interfaces of an immersed screen

In the context of plane-wave propagation, the concept of replacing a fluid region containing distributed inclusions with an effective medium is examined. Attention is focused on a screen region of finite thickness, and the behavior of the displacement and pressure fields at the screen interfaces is investigated. In this work, one shows that the first derivative of the displacement is discontinuous at the interfaces. This result, together with an appropriate effective constitutive equation, allows one to determine the pressure on either side of each screen interface. Next, assuming that pressure jumps are not acceptable, one finds an explicit expression for the effective acoustic impedance of the screen. Finally, a formula for the coherent energy dissipated inside the screen is derived.