= Acoustic-gravity propagation relation
{title2=$k_r^2\simeq(\omega^2-S_\ell^2)(\omega^2-N^2)/(c_s^2\omega^2)$}
In the <Cowling approximation> and local short-wavelength limit, the radial wave number satisfies $k_r^2\simeq(\omega^2-S_\ell^2)(\omega^2-N^2)/(c_s^2\omega^2)$. The <Lamb frequency> $S_\ell$ and <stellar buoyancy frequency> $N$ delimit acoustic and gravity-wave cavities. This leading interior relation does not replace the near-surface acoustic cutoff or the full gravitational boundary problem.
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