Wavelength

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The wavelength is the distance between repeating units of a wave pattern. It is commonly designated by the greek letter lambda (λ).

In a sine wave, the wavelength is the distance between peaks:

Image:Wavelength.png

The x axis represents distance, and I would be some varying quantity (for instance air pressure for a sound wave or strength of the electric or magnetic field for light), at a given point in time as a function of x.

Wavelength has an inverse relationship frequency, the number of peaks to pass a point in a given time. The wavelength is equal to the speed of the wave divided by the frequency of the wave. When dealing with electromagnetic radiation in a vacuum, this speed is the speed of light c, so the conversion becomes,

where:

λ = wavelength of an electromagnetic wave
c = speed of light = 3×10⁸ m/s
ν = frequency of the wave

For radio waves this relationship is easily handled with this formula: meters of wavelength = 300/frequency in megahertz (MHz)

When light waves (and other electromagnetic waves) enter a medium, their wavelength is reduced by a factor equal to the refractive index n of the medium, but the frequency of the wave is unchanged. The wavelength of the wave in the medium, λ' is given by:

where λ₀ is the vacuum wavelength of the wave. Wavelengths of electromagnetic radiation are usually quoted in terms of the vacuum wavelength, although this is not always explicitly stated.

Louis-Victor de Broglie discovered that all particles with momentum have a wavelength, called the \de Broglie wavelength. For a relativistic particle, this wavelength is given by

where h is the Planck constant, p is the particle's momentum, m is the particle's mass, and v is the particle's velocity.