= Elastic-cover frequency ratio for water waves
{title2=$F(k)^2=[1+Bk^4/(\rho g+\sigma k^2)]/[1+(a\rho_s/\rho)k]$}
In the specified thin-sheet deep-water model, bending stiffness adds restoring force while sheet <mass> adds inertia. Their ratio to an uncovered <gravity-capillary wave> gives the displayed expression. Added inertia first lowers <frequency> at small <wavenumber>; at formally large <wavenumber> bending produces a <frequency> ratio proportional to $k^{1/2}$. That formal asymptote must not be extrapolated past the range where a thin-sheet continuum description is valid.
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