= Solution
Let $\rho'$ and $p'$ be the density and <pressure> perturbations. Homentropy gives $p'=c_0^2\rho'$. The linearized mass and <momentum> equations are
$$
\rho'_t+\rho_0\nabla\cdot\mathbf u=0,
\qquad
\rho_0\mathbf u_t=-\nabla p'.
$$
For <potential flow>, $\mathbf u=\nabla\phi$, and the <momentum> equation integrates to
$$
p'=-\rho_0\phi_t,
$$
where a <function> of time has been absorbed into $\phi$. Substitution into mass conservation yields
$$
-\frac{\rho_0}{c_0^2}\phi_{tt}+\rho_0\nabla^2\phi=0,
$$
so
$$
\boxed{\phi_{tt}-c_0^2\nabla^2\phi=0.}
$$
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