Tensioned-sheet acoustic impedance (source code)

= Tensioned-sheet acoustic impedance
{title2=$Z=i\rho_0\omega/\gamma-i(Tk^2-m\omega^2)/\omega$}

A sheet of <mass> per area $m$ and <elastic-sheet tension> $T$ backed by an identical outgoing fluid half-space presents the stated <surface acoustic impedance> to the other half-space, using upward sheet <velocity> $i\omega\eta=-V$. The fluid term is its <normal acoustic impedance>; the remaining term is structural. Infinite <elastic-sheet tension> suppresses every fixed nonzero spatial wavenumber, but not $k=0$, whereas infinite <mass> suppresses even spatially uniform motion. A massless untensioned sheet between identical fluids is transparent.