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Elastic wave in an isotropic solid

Acoustic impedance

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.


Acoustic transmission through a uniform layer

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 3 / 39A / c / Solution

Acoustic transmission through a uniform layer

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Acoustic transmission through a uniform layer

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