Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 40C / c / iii / Solution

For a P-wave incident at angle $\theta$ from a liquid $(\rho,c,\lambda)$ onto $(\rho',c',\lambda')$, with transmitted angle $\theta'$ obeying <Snell law for elastic and acoustic waves>,
$$
R=\frac{\lambda'\sin2\theta-\lambda\sin2\theta'}
{\lambda'\sin2\theta+\lambda\sin2\theta'}.
$$
No reflection is equivalent to $\rho'c'\cos\theta=\rho c\cos\theta'$.

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 Incoming links: Displacement reflection from an interface between two inviscid elastic liquids