Newton's Formula for Speed of Sound Waves in Air

Sir Isaac Newton assumed that when sound propagates through air, the compressions and rarefactions form slowly enough that any heat generated during compression, and any heat lost during rarefaction, has time to fully exchange with the surroundings, keeping the temperature of the medium constant throughout -- that is, the process is isothermal. Under this assumption the air molecules, treated as an ideal gas, obey Boyle's law, $PV=\text{constant}$. Differentiating this relation gives $P\,dV+V\,dP=0$, which rearranges to $P=-V\,dP/dV=K_I$, defining $K_I$ as the isothermal bulk modulus of air; substituting this into the general elastic-wave speed formula $v=\sqrt{K/\rho}$ gives Newton's formula, $v=\sqrt{K_I/\rho}=\sqrt{P/\rho}$. Evaluating this at normal temperature and pressure (NTP), using $P=0.76\times13.6\times10^3\times9.8\ \text{N/m}^2$ and $\rho=1.293\ \text{kg/m}^3$ for air, predicts a theoretical speed of about 279.8 m/s, i.e. approximately 280 m/s. But the experimentally measured speed of sound in air at 0 degC is 332 …