Q.Using Laplace's corrected formula, calculate the speed of sound in air at STP, given the pressure $P=1.013\times10^{5}\ \text{Pa}$, the density of air $\rho=1.29\ \text{kg m}^{-3}$, and $\gamma=1.4$ for air.

Given: $P=1.013\times10^{5}\ \text{Pa}$, $\rho=1.29\ \text{kg m}^{-3}$, $\gamma=1.4$.

Using Laplace's formula $v_L=\sqrt{\gamma P/\rho}$:

Substitute the given $P$, $\rho$, and $\gamma$ directly into $v_L=\sqrt{\gamma P/\rho}$ and evaluate.

• Using Newton's formula ($v=\sqrt{P/\rho}$, omitting $\gamma$) by mistake, which under-predicts the speed by about 15-16%.
• Arithmetic slips when combining the powers of ten under the square root.