= High-pressure limit of magnetosonic waves
{title2=$v_s^2\gg v_a^2$}
= High-beta magnetosonic limit
{synonym}
For <sound speed> $v_s$ much larger than <Alfvén speed> $v_a$, and angle $\theta$ between the <wavevector> and <magnetic field>, the <fast magnetosonic wave> has $v_f^2=v_s^2+v_a^2\sin^2\theta+O(v_a^4/v_s^2)$. The <slow magnetosonic wave> has $v_{\rm slow}^2=v_a^2\cos^2\theta[1-(v_a^2/v_s^2)\sin^2\theta+O(v_a^4/v_s^4)]$. The fast mode is predominantly longitudinal sound. The slow mode becomes almost incompressible, polarized in the plane of the <wavevector> and <magnetic field>; the <Alfvén wave> is polarized perpendicular to that plane. The latter two are predominantly magnetic-tension waves with equal leading <phase speeds>.
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