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Wave Frequency from Wavelength

Wave frequency from speed and wavelength

Result

439.74 Hz

How it is calculated

The wave equation gives f = v ÷ λ, where v is the speed at which the wave travels (m/s), λ (lambda) is the wavelength, the distance between two successive crests (m), and f is the frequency in hertz (Hz), meaning cycles per second. The result is always shown in plain hertz with two decimals, never in kHz or MHz, so large frequencies appear as long numbers. Speed and wavelength must both be above zero. The speed depends on the medium: about 343 m/s for sound in air at 20 °C, about 299,792,458 m/s for light and radio waves in vacuum, and different values in water, steel or glass. The tool does not look up the speed for you; you supply it.

Worked example

A sound wave in air at about 20 °C travels at 343 m/s and its wavelength is 0.78 m. Divide the speed by the wavelength: 343 ÷ 0.78 ≈ 439.74. The frequency is 439.74 Hz, close to the 440 Hz concert A tuning note. In the same way a radio wave with a 3 m wavelength, travelling at 299,792,458 m/s, gives about 99,930,819.33 Hz, which is roughly 99.9 MHz.

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Common mistakes

  • Entering the wavelength in centimetres, nanometres or millimetres while the speed is in m/s. Convert the wavelength to metres first (500 nm is 0.0000005 m).
  • Using the speed of light for a sound wave, or the speed of sound for a radio wave. The speed has to be the one in the medium you are working with.
  • Reading the result as kHz or MHz. It is in hertz, so divide by 1000 or 1,000,000 yourself.
  • Forgetting that the speed of sound changes with temperature; using 343 m/s on a very cold or hot day gives a slightly wrong frequency.
  • Keeping the frequency of a wave that enters another medium. The frequency stays the same, but the speed and the wavelength change, so recompute with the new speed.

About this calculator

This calculator applies the fundamental wave equation, f = v / λ, which holds for every kind of wave — sound, light, radio and water — and simply says frequency and wavelength are inversely proportional at a fixed propagation speed v: double the wavelength and the frequency halves.

Radio engineers use it to convert between a transmitter's frequency and its antenna's physical wavelength, physicists use it to relate a photon's color to its frequency using the speed of light, and audio engineers use it to figure out the wavelength of a given musical pitch in air, which matters for room acoustics and speaker placement.

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Comments (1)

  • Editorial team

    To go the other way, divide the speed by the frequency to get the wavelength. This is how radio people size antennas: a 99.9 MHz FM signal has a wavelength of about 3.0 m, so a quarter-wave antenna is near 0.75 m, though real antennas are trimmed to fit. Remember that the speed you enter must match the medium. Is your wave sound, radio or light, and what speed did you use?

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