Laplace correction in the expression for the velocity of sound given by Newton's is needed because sound waves propagate adiabatically.

After correction, the velocity of sound formula,

$$\begin{gathered} v=\sqrt{\frac{\gamma P}{\rho }} \\ Where, \gamma = \mathrm{Adiabatic} \mathrm{index} \\ P=\mathrm{Pressure} \\ \rho =\mathrm{Density} \end{gathered}$$