At 0 °C and a pressure of 1.013 × 10⁵ Pa, the density of dry air is 1.293 kg/m³…

Step 1. Newton. $v = \sqrt{\dfrac{1.013 \times 10^5\ \text{Pa}}{1.293\ \text{kg/m}^3}} = \sqrt{78\,300\ \text{m}^2/\text{s}^2} = 280\ \text{m/s}$.

Step 2. Laplace. $v = \sqrt{1.40} \times 280\ \text{m/s} = 1.183 \times 280\ \text{m/s} = 331\ \text{m/s}$.

Step 3. The error. $1 - \dfrac{280\ \text{m/s}}{331\ \text{m/s}} = 0.155$, so Newton was too low by $15.5$ percent.

Why. Newton used the isothermal bulk modulus $p$. The true changes are adiabatic, with the bulk modulus $\gamma p$. Every speed from Newton's formula is too low by the same factor, $\sqrt{\gamma}$.