Acoustic transmission through a uniform layer
= Acoustic transmission through a uniform layer
A layer of impedance $Z_1$, wavenumber $k_1$, and thickness $L$ between identical media of impedance $Z_0$ has pressure-amplitude transmission coefficient
$$
|T|=\left[\cos^2(k_1L)+\frac14\left(\frac{Z_1}{Z_0}+\frac{Z_0}{Z_1}\right)^2\sin^2(k_1L)\right]^{-1/2}.
$$
It transmits perfectly at the layer resonances $k_1L=n\pi$, irrespective of the impedance mismatch.