= Solution
The <tight-coupling approximation> requires the positive scattering rate $\kappa=-\dot\tau$ to exceed both $k$ and the <conformal Hubble parameter>. The <photon-baryon velocity slip> and <photon quadrupole> are then small, and the leading fluid motion has $v_b=v_\gamma=v$. One must combine the equations before setting the slip to zero: a small slip times a large collision rate can exert a finite force.
Add the <photon Euler equation> to $R$ times the <baryon Euler equation with Thomson drag>. The collisions cancel and, neglecting $\Theta_2$ at this order, the result is
$$
(1+R)\dot v+\mathcal H Rv+\frac{k}{4}\delta_\gamma+(1+R)k\psi=0.
$$
Since $\dot R=\mathcal H R$, the common velocity obeys
$$
\boxed{\dot v_\gamma+\frac{\dot R}{1+R}v_\gamma+\frac{k}{4(1+R)}\delta_\gamma+k\psi=0.}
$$
The inertia of the <baryons> reduces the <photon-baryon sound speed> to $c_s^2=1/[3(1+R)]$.
Differentiate the <photon continuity equation> and substitute this velocity equation:
$$
\ddot\delta_\gamma=\frac43k\dot v_\gamma+4\ddot\phi=-\frac{\dot R}{1+R}(\dot\delta_\gamma-4\dot\phi)-\frac{k^2}{3(1+R)}\delta_\gamma-\frac43k^2\psi+4\ddot\phi.
$$
Thus the <photon-baryon acoustic oscillator> is
$$
\boxed{\ddot\delta_\gamma+\frac{\dot R}{1+R}\dot\delta_\gamma+\frac{k^2}{3(1+R)}\delta_\gamma=4\ddot\phi+\frac{4\dot R}{1+R}\dot\phi-\frac43k^2\psi.}
$$
The terms on the right drive the oscillation gravitationally; the first-derivative term comes from changing <baryon> inertia. Diffusion damping enters only beyond this leading <tight-coupling approximation>.
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