Speed of Sound in Gases

Ideal-gas speed of sound

Sound in a gas is an adiabatic compression wave. For an ideal gas the speed depends only on absolute temperature, the ratio of specific heats γ and the molar mass M, not on pressure:

For dry air this reduces to the familiar engineering form:

Humidity

Water vapour (M = 18 g/mol) is lighter than dry air (29 g/mol), so humid air carries sound slightly faster, typically 0.1–0.6 % more, increasing strongly with temperature. Here the water-vapour mole fraction is derived from the ISO 9613-1saturation pressure formula, and the mixture's γ is computed from the heat capacities of its components (diatomic air withC_v = 5/2\cdot R, water vapour with C_v \approx 3R).

Light gases, fast sound

Helium and hydrogen have tiny molar masses, so sound travels about three and four times faster than in air. That shifts the resonances of the vocal tract upward, the famous squeaky helium voice, while the vocal-fold pitch itself barely changes. Heavy gases like CO₂ or SF₆ do the opposite.

Limitations

γ is treated as constant; at high temperatures polyatomic gases (CO₂, CH₄) excite vibrational modes and γ drops, so results above ~200 °C are approximate.