Sound-crossing time ($t_s\sim L/c_s$)

The sound-crossing time is the characteristic time needed for an acoustic wave to cross a region of size $L$. If the speed of sound is nearly uniform, $t_s\sim L/c_s$; along a specified path through a nonuniform medium, the travel time is $\int ds/c_s(s)$.

This is also a timescale for communicating a change of pressure. A gas compressed much more slowly than its sound-crossing time can often adjust toward mechanical equilibrium throughout the container. A rapid push can instead create substantial pressure differences and propagating waves. Comparing a collapse or heating timescale with $t_s$ helps determine whether a spatially uniform pressure approximation is plausible. The crossing time itself does not guarantee equilibration: reflections, geometry and damping determine what happens after the disturbance arrives.