The one equation
In dry air at 20°C sound moves at about 343 m/s, so wavelength (in meters) is 343 divided by the frequency in hertz. High notes have short waves, low notes have long ones. Concert A at 440 Hz works out to 343 ÷ 440 ≈ 0.78 m (about 78 cm).
Wavelength in air across the hearing range
| Frequency | Wavelength (air, 20°C) | Note |
|---|---|---|
| 20 Hz | 17.2 m | Lowest audible; hard to localize |
| 100 Hz | 3.43 m | Deep bass |
| 440 Hz | 0.78 m | Concert A (A4) |
| 1 kHz | 0.343 m | Reference tone |
| 10 kHz | 3.43 cm | High treble |
| 20 kHz | 1.72 cm | Top of hearing |
To go the other way, use frequency = speed ÷ wavelength. A half-meter wave in air is 343 ÷ 0.5 ≈ 686 Hz.
Two things that shift the answer
- Temperature. The speed of sound in air is about 331.4 + 0.6 × T (°C). Warmer air is faster, so the same note has a slightly longer wave on a hot day than a cold one.
- Medium. Sound is far faster in denser, stiffer material — roughly 1480 m/s in fresh water and 5800 m/s in steel. Keep the speed matched to the medium or the wavelength will be wildly off.
Common questions
How do I calculate the wavelength of a sound?
Divide the speed of sound by the frequency. In room-temperature air that is 343 meters per second divided by the frequency in hertz. A 100 Hz tone has a wavelength of 3.43 meters; a 1000 Hz tone is 0.343 meters.
Does temperature change the wavelength?
Yes, because it changes the speed of sound. Speed in air is about 331.4 plus 0.6 times the temperature in Celsius, so warmer air is faster and stretches the wavelength slightly. Around a 6 meters per second gain for every 10 degrees.
Why do bass notes need big rooms and subwoofers?
Low frequencies have long wavelengths. A 30 Hz note is over 11 meters long, so it interacts with whole rooms and is hard to localize. High frequencies, at centimeters long, are directional and easy to point.
What is the wavelength of sound in water versus air?
Sound travels about 1480 meters per second in fresh water, more than four times faster than in air. So at the same frequency the wavelength in water is roughly four times longer than in air.
