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Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2022

Paper 2

Eliminating $T$ from the two boundary conditions gives
$$
\frac{1+R}{1-R}
=\frac{\lambda'k'\cos\theta}
{\lambda k\cos\theta'}.
$$
The <Snell law for elastic and acoustic waves> implies
$$
\frac{k'}k=\frac{\sin\theta}{\sin\theta'}.
$$
Therefore the <displacement reflection from an interface between two inviscid elastic liquids> is
$$
\boxed{
R=\frac{\lambda'\sin2\theta-\lambda\sin2\theta'}
{\lambda'\sin2\theta+\lambda\sin2\theta'}}.
$$

Solution

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

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

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

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