Solution
= Solution
The <linear homentropic acoustic equations> are
$$
\rho'_t+\rho_0\nabla\mathbin\cdot\mathbf u=0,
\qquad
\rho_0\mathbf u_t=-\nabla p',
\qquad
p'=c_0^2\rho'.
$$
Differentiate the first equation in time, take the divergence of the second, and use the third. This eliminates $\rho'$ and $\mathbf u$ and gives the <acoustic pressure wave equation>
$$
\boxed{p'_{tt}=c_0^2\nabla^2p'.}
$$