Flexural wave
= Flexural wave
{title2=$\omega^2=(B/m)k^4$}
For a thin plate with areal mass $m$ and <bending stiffness> $B$, small free transverse disturbances satisfy $m\eta_{tt}+B\nabla^4\eta=0$. A <plane wave> of tangential <wavenumber> $k$ therefore satisfies
$$
\omega^2=(B/m)k^4.
$$
The frequency is quadratic in <wavenumber>, so these waves are dispersive. Matching this free-wave relation cancels the plate's inertial and bending response in an acoustic transmission problem.