= Solution
Write $\rho=\rho_0+\widetilde\rho$, $p=p_0+\widetilde p$, and let $\widetilde{\mathbf u}$ be small. Linearized mass and momentum conservation are
$$
\partial_t\widetilde\rho+\rho_0\nabla\cdot\widetilde{\mathbf u}=0,
\qquad
\rho_0\partial_t\widetilde{\mathbf u}=-\nabla\widetilde p.
$$
The linearized equation of state is
$\widetilde p=c_0^2\widetilde\rho$. Differentiate the first equation in time and eliminate the velocity with the second to obtain the <wave equation>
$$
\boxed{\partial_t^2\widetilde p-c_0^2\nabla^2\widetilde p=0}.
$$
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