= Solution
Sound compressions in air are approximately adiabatic, giving $c_s^2=(\partial p/\partial\rho)_s=\gamma p/\rho$. With $p=\rho RT/M$,
$$
\boxed{T=\frac{Mc_s^2}{\gamma R}\simeq255\ \mathrm K\simeq-18\ ^\circ\mathrm C}.
$$
Here dry air is approximated as a diatomic <ideal gas> with $\gamma=7/5$ and <molar mass> $M\simeq0.029\ \mathrm{kg\,mol^{-1}}$. The ideal-gas law alone is insufficient without this adiabatic response and mean molecular <mass>; humidity and composition affect a more precise inference.
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