What is Acoustic perturbation?

A fluid at rest, of uniform pressure $P_0$ and density $\rho_0$, is disturbed: $P = P_0 + p(M, t)$, $\rho = \rho_0 + \rho_1(M, t)$, velocity $\vect v(M, t)$. The acoustic approximation keeps only the first order in the small quantities $p$ (the overpressure, or acoustic pressure), $\rho_1$ and $\vect v$: $|p| \ll P_0$, $|\rho_1| \ll \rho_0$, $v \ll c$, and the transformation undergone by each fluid particle is so fast that it exchanges no heat: it is isentropic, with the compressibility $\chi_S = \frac1\rho\bigl(\frac{\partial\rho}{\partial P}\bigr)_S$. Gravity is neglected.