Solution
= Solution
Set $\delta_R=e^{-S}u$ and neglect $S''$, $(S')^2$, and slow variation relative to $k^2$. Cancelling the first <derivative> gives $S'=\alpha k/(2\mathcal H)$, hence $S=\int^\tau\alpha k/(2\mathcal H)d\tau'$, and $u''+(c^2k^2/3)u\simeq0$. Thus acoustic oscillations are exponentially damped, unlike pressureless matter perturbations, which have a growing mode.