Ray asymptotics of a clamped elastic waveguide mode

A shear-horizontal wave mode has ${\omega }_n(k)=c_s\sqrt{k^2+(n\pi /h{)}^2}$. At $x=Vt$ with $0<|V|<c_s$, a nondegenerate stationary Fourier phase gives generic $t^{-1/2}$ decay. Faster rays have no stationary point; compactly supported data give eventual zero by finite propagation speed.