 Solution

Sound compressions in air are approximately adiabatic, giving $c_s^2=(\partial p/\partial \rho {)}_s=\gamma p/\rho$. With $p=\rho RT/M$,Here dry air is approximated as a diatomic ideal gas with $\gamma =7/5$ and molar mass $M\simeq 0.029\mathrm{kg}\mathrm{mo}{\mathrm{l}}^{-1}$. The ideal-gas law alone is insufficient without this adiabatic response and mean molecular mass; humidity and composition affect a more precise inference.