Fluid-loaded membrane edge scattering
= Fluid-loaded membrane edge scattering
A pinned semi-infinite membrane scatters an incoming guided mode into reflected guided modes and outgoing sound. For unit incident displacement the scattered endpoint value is $-1$. Its <Half-range Fourier transform> therefore has nonzero endpoint terms even though the total displacement vanishes. The <Wiener-Hopf equation> kernel is $2/(m\omega^2-Tk^2)+\gamma/(\rho_0\omega^2)$ with the outgoing branch $\gamma^2=k^2-\omega^2/c_0^2$.