= Debye sound speed
{c}
{title2=$3/v_D^3=1/v_L^3+2/v_T^3$}
The effective isotropic acoustic speed used to replace separate branches in the <Debye model>. With atomic number density $n$, counting three branches gives $k_D=(6\pi^2n)^{1/3}$ and $\omega_D=v_Dk_D=k_B\theta_D/\hbar$. Matching the low-frequency <density of states> for one longitudinal and two transverse branches gives the displayed inverse-cube average. A <Debye temperature> alone does not determine both individual <sound speeds>.
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