Speed of Sound and Wavelength Calculator

Speed of sound in air

Sound travels through air as a pressure wave, and its speed depends on the air temperature. Treating dry air as an ideal gas:

v = √(γ × R × T / M)

Here γ = 1.4 is the ratio of specific heats of air, R = 8.314 J/(mol·K) is the gas constant, M = 0.0289644 kg/mol is the molar mass of air and T is the temperature in kelvin. For everyday temperatures the approximate form v ≈ 331.3 + 0.606 × T (T in degrees Celsius) is good enough.

Results: 331.3 m/s at 0 °C, 340.3 m/s at 15 °C, 343.2 m/s at 20 °C and 349.0 m/s at 30 °C. The speed of sound does not depend on air pressure or on the frequency of the sound.

Wavelength

Wavelength is speed divided by frequency: λ = v / f. At 20 °C a 440 Hz tone has a wavelength of 343.2 / 440 = 0.78 m.

How far away is the lightning?

Light arrives almost instantly, while sound covers about 340 metres each second. Count the seconds between the flash and the thunder and multiply by the speed of sound. Three seconds is roughly one kilometre.

Echo

When sound bounces off an obstacle it covers the distance twice. With the obstacle at distance d, the echo arrives after 2 × d / v. Sonar and ultrasound ranging work on this principle.

Limits

The calculation is for dry air. Humidity raises the speed of sound slightly (by less than half a percent at room temperature). Wind changes the speed of sound relative to the ground. The 1482 m/s figure for water is approximate, for fresh water at 20 °C. For solids and other gases, enter the speed yourself.