An elastic solid occupies the region $y<0$. The wave speeds in the solid are $c_{\mathrm{p}}$ and $c_{\mathrm{s}}$. A P-wave with dilatational potential

$$\phi=\exp \left\{i k\left(x \sin \theta+y \cos \theta-c_{\mathrm{p}} t\right)\right\}$$

is incident from $y<0$ on a rigid barrier at $y=0$. Obtain the reflected waves.

Are there circumstances where the reflected S-wave is evanescent? Give reasons for your answer.