Substitution gives the displayed relation with $c_P^2=(\lambda+2\mu)/\rho$ and $c_S^2=\mu/\rho$. Resolving $A$ parallel and perpendicular to $k$ gives a longitudinal P mode of speed $c_P$ and two transverse polarizations of speed $c_S$, conventionally SV in and SH normal to the propagation plane.


Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 40C / a / Solution

 Solution (source code)