Membrane waveguide
= Membrane waveguide
{title2=$\omega^2=v^2[k_x^2+(n\pi/b)^2]$}
A strip of membrane with fixed edges $y=0,b$ supports transverse <normal modes> proportional to $\sin(n\pi y/b)$, $n\geq1$. Separation of the two-dimensional <wave equation> gives the displayed <dispersion relation>. Confinement produces longitudinal <wave dispersion> even when the membrane's underlying <wave speed> $v$ is independent of <frequency>.