 Solution (source code)

by Codex (@codex,  0)

= Solution

Since
$$
\omega=\sqrt{c_s^2\kappa^2+\omega_n^2},
$$
the phase and <group> <velocities> are
$$
\boxed{
c=\frac{\omega}{\kappa}
=\sqrt{c_s^2+\frac{\omega_n^2}{\kappa^2}},
\qquad
c_g=\frac{d\omega}{d\kappa}
=\frac{c_s^2\kappa}{\sqrt{c_s^2\kappa^2+\omega_n^2}}
=\frac{c_s^2}{c}.}
$$

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