The speed of sound and thunder: what actually determines the delay
Updated · 7 min read
Sound travels at 343 meters per second at 20 °C in dry air, but the true value depends on temperature, humidity, pressure and CO₂. The Cramer (1993) equation captures all four and is accurate to about 300 parts per million, roughly 30 times better than the common 331.3 + 0.606T approximation in humid conditions.
What is the speed of sound in air?[1]
Sound travels at 343.4 meters per second (1,235 km/h or 767 mph) in dry air at 20 °C and standard pressure. The value rises with temperature by roughly 0.6 m/s per degree Celsius, and rises slightly further as humidity increases.
Most references quote a single number because the variation seems small. Over the distances thunder travels, though, it stops being small. A 1 m/s error across 10 km shifts the arrival time by about 85 milliseconds, and the seasonal spread is closer to 20 m/s.
Does humidity make sound travel faster or slower?
Humid air carries sound faster than dry air. Water vapor has a molecular mass of 18, lighter than the nitrogen (28) and oxygen (32) it displaces, so humid air is less dense and sound moves through it more quickly. At 20 °C, saturated air carries sound 1.2 m/s faster than dry air.
This surprises most people, who assume damp air is heavier. The confusion comes from humid air feeling heavier, which is a thermal comfort effect rather than a density one.
The effect grows sharply with temperature because warm air holds far more moisture. At 0 °C the difference between dry and saturated air is negligible, but at 30 °C saturated air carries sound about 2 m/s faster. That is enough to shift a 10 km thunder arrival by 160 milliseconds.
What is the Cramer equation?
The Cramer (1993) equation calculates the speed of sound from temperature, pressure, water-vapor content and CO₂ concentration using sixteen coefficients. Published in the Journal of the Acoustical Society of America, it is accurate to about 300 parts per million between 0 and 30 °C, the reference standard for precise acoustic work.
The simple approximation everyone learns, 331.3 + 0.606 × temperature, ignores humidity entirely. In dry air it is close enough. In hot, humid air, which is exactly what produces thunderstorms, it drifts by around 2 m/s.
This site uses the full Cramer equation rather than the approximation, with live temperature, humidity and pressure fetched for both your position and the strike location. Over a 10 km path in humid summer air, that is the difference between a thunder estimate that is 160 milliseconds out and one that is not.
| Method | Inputs | Error at 30 °C, humid |
|---|---|---|
| Divide by 3 or 5 | none | up to ±8% |
| 331.3 + 0.606T | temperature | about 2 m/s (160 ms per 10 km) |
| Cramer 1993 | temperature, humidity, pressure, CO₂ | about 300 ppm |
How does wind change thunder timing?
Wind carries sound with it, adding directly to the propagation speed. A 10 m/s tailwind blowing from the storm toward you delivers thunder about 0.85 seconds early over 10 km. The same wind against the path delays it by a similar amount and shortens how far the thunder carries.
Only the component of the wind along the strike-to-listener path matters. A crosswind blowing perpendicular to that line has almost no effect on arrival time.
Wind also skews the audible range asymmetrically. Downwind, the wavefront bends back toward the ground and thunder carries noticeably further than the usual 16 km limit. Upwind, refraction lifts it away sooner. This is why a storm can be clearly audible in one direction and silent in another at the same distance.
References
- The variation of the specific heat ratio and the speed of sound in air with temperature, pressure, humidity, and CO2 concentrationJournal of the Acoustical Society of America 93(5), 2510-2516, 1993 · doi:10.1121/1.405827
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