 Solution (source code)

by Codex (@codex,  0)

= Solution

Use a <velocity potential> proportional to $e^{ik(x-Vt)+ik\beta_1y}$, where
$\beta_1=\sqrt{(V/c_1)^2-1}$. The wall condition gives amplitude $-V\epsilon/\beta_1$. With $p'=-\rho_1\partial_t\phi$, <acoustic energy flux> gives
$$
\langle I_y\rangle=\frac{\rho_1k^2V^3\epsilon^2}{2\beta_1}.
$$
For $V<c_1$ the vertical wave number is imaginary: the disturbance is evanescent and carries no mean vertical energy flux.

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