If the self-gravity is ignorable, equation (2.35)

where we assumed the gas is isothermal, these two equations describe the propagation and growth of perturbations. If the gas acts adiabatically, replace with .

Making
(2.40) and
(2.41)
vanishes and we obtain

(2.43) | |||

(2.44) |

equation (2.42) has a solution that a wave propagates with a phase velocity of . Since the displacement ( ) is parallel to the propagation direction , and the restoring force comes from the pressure, this seems