Guided SH modes between rigid and free planes

For a layer $0<z<h$ with rigid lower boundary and traction-free upper boundary, an SH mode
$u_y=Y(z)e^{i(\kappa x-\omega t)}$ hasand dispersionIts cutoff is ${\omega }_n=c_s{q}_n$, its phase speed is $\omega /\kappa$, and its group speed is $c_s^2\kappa /\omega$.