= Acoustic wave on a tensioned massive membrane
= Acoustic membrane wave
{synonym}
A membrane of mass per area $m$ and tension $T$ separating two identical acoustic half-spaces has evanescent modes with
$$
\left(m+\frac{2\rho_0}{\sqrt{k^2-\omega^2/c_0^2}}\right)\omega^2=Tk^2.
$$
The second term is the <added mass of an evanescent fluid layer> contributed by both sides. Hence the phase speed is below the vacuum membrane speed $\sqrt{T/m}$, and for $k\to0$ it obeys $c\sim\sqrt{Tk/(2\rho_0)}\to0$. Pressure and normal velocity are in quadrature, so the mean normal <acoustic energy flux> vanishes.
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