thermodynamics - How is sound wave quasistatic?

Sound waves is approximately adiabatic; however, for any adiabatic compression, one needs to assume quasi-static process in order to derive $V^rP=\text{Constant}$, and then obtain the speed of sound $v_s=\sqrt{\frac{rP}{\sigma}}$ (from $v_s=\sqrt{\frac{B}{\sigma}}$ , where $B=\frac{\Delta P}{-\Delta V/V}$ , $\sigma$ is density of medium.)

but given sound wave is so fast, how come this become a good approximation?