= Reflection pole of a fluid-loaded membrane
{title2=$D=Tk^2-m\omega^2-2\rho_0\omega^2/\gamma=0$}
A free <acoustic membrane wave> is a zero of the outgoing <dispersion relation> $D$. At this zero, the impedance seen from one side equals the negative of that side's outgoing <normal acoustic impedance>. Thus the continued by <analytic continuation> <reflection coefficient> has a pole. A real guided mode is evanescent normal to the sheet; a complex root can describe a leaky mode. The pole describes nontrivial homogeneous motion with no incoming wave, rather than unbounded passive reflection at an ordinary real incidence angle.
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