How fast sound travels
Sound is a pressure wave that moves through air, water or solids. In air its speed depends mainly on temperature: warmer air carries sound faster because its molecules move more quickly. At 68 °F (20 °C), sound covers about 343 meters per second, a mile in under five seconds. Air pressure and altitude, on their own, have almost no effect.
The formula
v = 331.3 × √(1 + T ÷ 273.15), in m/s, with T in °C.
This formula for dry air is accurate to within a fraction of a percent for everyday temperatures. As a rule of thumb, the speed rises by about 0.6 m/s per °C, or 1.1 ft/s per °F. Humidity adds a little: in very humid air at 86 °F the speed is about 0.3% higher.
Worked example
The air is at 68 °F, and you want to know how long a sound takes to travel 1 mile.
- 68 °F = 20 °C.
- v = 331.3 × √(1 + 20 ÷ 273.15) = 343.2 m/s, about 768 mph or 1,126 ft/s.
- Time over 1 mile (1,609 m): 1,609 ÷ 343.2 = 4.69 seconds.
- An echo from a cliff 1 mile away would come back after 9.38 seconds.
Speed of sound at different temperatures
| Air temperature | Speed of sound |
|---|---|
| −4 °F (−20 °C) | 319 m/s, 713 mph |
| 32 °F (0 °C) | 331 m/s, 741 mph |
| 68 °F (20 °C) | 343 m/s, 768 mph |
| 104 °F (40 °C) | 355 m/s, 793 mph |
In other materials
Sound moves much faster in liquids and solids, which are harder to compress: about 1,480 m/s in fresh water, 1,520 m/s in seawater, around 3,800 m/s in hardwood along the grain and about 5,900 m/s in steel. That is why you can hear an approaching train in the rails before you hear it in the air.
Practical uses
- Thunderstorms: count the seconds between lightning and thunder and divide by 5 to get miles, or by 3 for kilometers.
- Echoes and sonar: measuring the time an echo takes gives the distance to a wall or the seabed.
- Music and audio: the speed of sound sets the wavelength of each note and the delay between speakers in a large hall.
- Aviation: the Mach number compares an aircraft’s speed with the local speed of sound. At cruising altitude, where the air is around −70 °F, Mach 1 is only about 660 mph.