= Rigid-backed shear-wave dispersion
{title2=$\tan(mh)=-\mu_1m/(\mu_2\ell)$}
A layer with <shear modulus> $\mu_1$ and <wave speed> $c_1$ lies between a rigid support and a <half-space> with <shear modulus> $\mu_2$ and <wave speed> $c_2>c_1$. A trapped <antiplane shear> <normal mode> has layer amplitude $A\sin(my)$ and exterior amplitude $A\sin(mh)e^{-\ell(y-h)}$, where $m=k\sqrt{c^2/c_1^2-1}$ and $\ell=k\sqrt{1-c^2/c_2^2}$. Continuity of <displacement field> and <traction> gives the displayed <dispersion relation>. It requires $c_1<c<c_2$ and differs from a <Love wave> with a free boundary.
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