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Wavelength Calculator – Calculate ? from Frequency & Speed

Easily find wavelength given frequency and wave speed using the fundamental wavelength equation. Perfect for calculating radio, sound, or light waves.

Calculation Results

Wavelength

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Frequency

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Period

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Wave Speed

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Advanced Properties

Wavenumber (k)

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Spectroscopic wavenumber (m?¹)

Angular Freq (?)

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rad/s

Wavelength Formulas & Physics

Wavelength Formula

? = v / f

Where: ? = wavelength (m), v = wave speed (m/s), f = frequency (Hz)

Wavelength (?) is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is inversely proportional to frequency: as frequency increases, wavelength decreases.

What is Wavenumber (k)?

Wavenumber (k) represents the spatial frequency of a wave, describing how many cycles exist per unit distance. The formula used here is k = 1 / ? (spectroscopic definition), though in physics (angular wavenumber), it's often defined as k = 2p / ?. This calculator provides the spectroscopic wavenumber in m?¹.

What is Angular Frequency (?)?

Angular frequency (?) measures the rate of rotation or oscillation in radians per second. It is related to ordinary frequency (f) by the equation: ? = 2pf. It is commonly used in harmonic motion and wave mechanics analysis.

Photon Energy (E)

For electromagnetic waves (light), energy is directly proportional to frequency. Using Planck's constant (h), the energy of a single photon is calculated as: E = h · f or E = h · c / ?. This output is automatically displayed when the wave speed is close to the speed of light.

Derived Formulas

  • Frequency: f = v / ?
  • Wave Speed: v = f · ?
  • Period: T = 1 / f

Related Tools

Need to solve for other variables? Use our specialized tools: Frequency Calculator or check our Physics category for more.

Frequently Asked Questions

1. What is the difference between wavelength and period?
Wavelength (?) is the spatial distance between two peaks of a wave, measured in meters. Period (T) is the time it takes for one complete cycle to pass a point, measured in seconds. They are related by speed: ? = v · T.
2. How does the medium affect wavelength?
The medium determines the speed of the wave. For example, sound travels faster in water than in air. Since frequency usually stays constant (determined by the source), a change in speed causes a direct change in wavelength (? = v / f).
3. What is the wavenumber?
The wavenumber is the number of waves per unit distance. It is the spatial analog of frequency. In spectroscopy, it is calculated as k = 1/?, while in wave mechanics, it is often k = 2p/?. This calculator displays k = 1/?.