The speed of sound: how fast it travels and what changes it

Sound travels at about 343 metres per second in dry air at 20 °C: roughly 1 km in 2.9 seconds, or one mile in 4.7 seconds. The main thing that changes that figure in air is temperature; colder air is slower, warmer air is faster, and air pressure on its own has almost no effect. In water sound is over four times faster, and in steel more than 17 times faster. The speed of sound calculator gives the speed for any air temperature or material, plus travel times and wavelengths.

The speed of sound in air

For dry air, the speed is very close to c ≈ 331.3 × √(1 + T/273.15) m/s, where T is the temperature in °C. Near everyday temperatures that simplifies to c ≈ 331.3 + 0.606 × T. Some reference points:

• −20 °C: about 319 m/s
• 0 °C: about 331 m/s
• 20 °C: about 343 m/s (1,235 km/h, 767 mph)
• 40 °C: about 355 m/s

Humidity makes sound very slightly faster, because water vapour molecules are lighter than nitrogen and oxygen. The effect is well under 1%, and I include it in the calculator as a small approximate correction. Wind matters more for practical purposes: sound carried downwind travels at its own speed plus the wind speed, and wind and temperature layers can bend sound, which is why distant noises carry further on some days than others.

Why temperature, not pressure

Sound is a pressure wave passed from molecule to molecule, so its speed depends on how strongly the gas pushes back when squeezed compared with how heavy it is. In an ideal gas, raising the pressure at constant temperature raises the density by the same proportion, and the two effects cancel. What is left depends on how fast the molecules are already moving, which is set by temperature. That is why the speed of sound at the top of a mountain on a warm day is the same as at sea level at the same temperature. It falls with altitude in the real atmosphere only because the air there is usually colder. If you think in Fahrenheit, the temperature converter turns your reading into °C for the formula.

Water, steel and other materials

Liquids and solids are much stiffer than air, so although they are denser, sound moves through them far faster. Typical values:

• Fresh water at 20 °C: about 1,481 m/s;
• Seawater: around 1,520 m/s, varying with temperature, salinity and depth;
• Steel: around 6,000 m/s for compression waves;
• Helium: about 1,000 m/s, which is why it raises the pitch of resonances in your voice.

Real materials vary with composition and temperature, so treat these as typical rather than exact. The difference is easy to notice: put your ear to a long metal railing while someone taps the far end, and you hear the tap through the metal before the sound arrives through the air.

Thunder, echoes and delays

Light arrives almost instantly, so the gap between a lightning flash and its thunder measures how far away the strike was. The US National Weather Service rule is about 5 seconds per mile; in metric, about 3 seconds per kilometre. The lightning distance calculator does the counting with a tap timer. Echoes work the same way in both directions: a wall 170 m away returns a shout after about one second. In music and live sound, the same speed sets delays between speakers at large venues, and the wavelength of a note is speed divided by frequency, so concert A at 440 Hz is about 78 cm long in air. The wavelength and frequency calculator does that sum for any wave, and Why A is 440 Hz: how concert pitch was standardised covers the pitch itself.

Mach numbers and altitude

A Mach number is speed divided by the local speed of sound. Mach 1 is not a fixed speed: at cruising altitude, where the air in the standard atmosphere is about −56.5 °C, the speed of sound is only about 295 m/s, roughly 14% slower than at sea level on a mild day. An aircraft can therefore be closer to Mach 1 at altitude than its ground speed suggests. For the much faster speed of light and the distances it covers, see How far is a light-year? Measuring distances in space.