Factors Affecting Speed of Sound in Gases

Rewriting the Laplace speed-of-sound formula using the ideal gas equation of state, $PV=\mu RT$ (with $\mu$ the number of moles, $R$ the universal gas constant), and substituting $\rho=M/V$ (with $M$ the molar mass) gives the fully explicit form $v=\sqrt{\gamma RT/M}$, which makes each of the following practical dependencies transparent. Effect of pressure: at a fixed temperature, if pressure varies then density varies in exact proportion, so the ratio $P/\rho$ -- and hence the speed of sound -- stays constant; sound speed is therefore independent of pressure alone (though the speed does genuinely differ at different altitudes, because temperature, not pressure directly, differs there). Effect of temperature: since $v\propto\sqrt{T}$, sound speed increases with the square root of the absolute temperature; using a binomial expansion around 0 degC (273 K), this can be approximated by the linear relation $v=(331+0.61t)\ \text{m/s}$ for temperature $t$ in degrees Celsius, i.e. sound speed rises by about 0.61 m/s for every 1 degree Celsius increase, because warmer molecules carry more thermal energy and vibrate faster. Effect of density: comparing two gases at the same temperature and pressure but different densities $\rho_1,\rho_2$ (and the same $\gamma$) gives $v_1/v_2=\sqrt{\rho_2/\rho_1}$ -- sound travels more slowly through a denser gas. Effect of moisture (humidity): moist air is about 0.625 times as dense as dry air at the same pressure, so increasing humidity lowers air densit …