Speed of Sound by Temperature

Speed of sound vs air temperature

In dry air at sea level, sound speed tracks v = 331.3 + 0.606 · T(°C) m/s. That puts you at roughly 343 m/s at 20 °C, 331 m/s at 0 °C, and about 297 m/s at -50 °C, the sort of temperature you'd see on a typical commercial cruise. Where does the linear version come from? The full ideal-gas equation, v = √(γ·R·T / M), with γ=1.4 for diatomic air, R=8.314 J/(mol·K), M=0.029 kg/mol and T measured in kelvin. One consequence worth keeping in mind: Mach 1 varies with altitude and temperature, so a fighter doing Mach 1 at sea level is, in absolute terms, faster than one at 11 km up.

Applications

It shows up in supersonic aviation, where sonic boom thresholds hang on the local sound speed. In sonar, too: water carries sound at around 1480 m/s, far quicker than air does. Musical acoustics feels it whenever a room warms up and the wind instruments drift out of tune. And seismology leans on it heavily, reading P-wave and S-wave speeds to infer the temperature and makeup of Earth's interior.

FAQ

Why does cold air slow sound down? Sound speed scales with √T (absolute temperature). When the air is cold the molecules are sluggish, so they hand a pressure pulse along to the next one more slowly.

Is the linear formula accurate? It stays within ±0.5% from -20 °C to +40 °C, which covers most ground-level acoustics anyway. Step outside that band and you'll want the √(γRT/M) form instead.

Does pressure matter? For an ideal gas, no. Sound speed comes down to temperature and what the gas is made of, and pressure drops out of the equation.

Why is Mach 1 lower at altitude? Colder air, plain and simple. Up at 11 km cruise (-56 °C), Mach 1 works out to about 295 m/s, against 343 m/s down at sea level.