Speed of Sound in Air

Speed of sound in air: temperature dependence

For dry air at sea level, the speed of sound is well approximated by v = 331.3 + 0.606 · T(°C) m/s. At 20 °C ≈ 343 m/s; at 0 °C ≈ 331 m/s; at 35 °C ≈ 352 m/s. The general ideal-gas formula is v = √(γ·R·T / M), where γ=1.4 for diatomic air, R=8.314 J/(mol·K) is the universal gas constant, M=0.029 kg/mol is the molar mass of air, and T is absolute temperature in kelvin. Sound does not propagate in vacuum — it needs a material medium. Mach 1 equals the local sound speed, which depends on altitude and temperature. Lightning trick: divide the seconds between flash and thunder by 3 to get distance in km (sound travels ~1 km every 3 s).

Applications: music, sonar and aviation

Sound speed shapes musical instruments (organ pipes, flutes — pitch depends on temperature, why orchestras tune after warming up), sonar in submarines, medical ultrasound (~1.5 MHz in soft tissue), supersonic aviation (sonic booms when crossing Mach 1), and architectural acoustics (concert hall reverberation times).

FAQ

Does humidity affect sound speed? Yes, slightly — humid air is less dense, so sound travels a bit faster. The effect is small (~0.4% at 100% humidity vs dry).

Why is sound faster in water? Water is denser but also far stiffer (less compressible). Speed in water is ~1480 m/s; in steel ~5000 m/s — stiffer media beat denser ones.

Does altitude matter? Indirectly — temperature drops with altitude (about 6.5 °C per km in the troposphere), reducing sound speed. Pressure alone doesn't affect it for an ideal gas.

How fast is Mach 2? Twice the local sound speed. At sea level around 20 °C, Mach 2 ≈ 686 m/s ≈ 2470 km/h.