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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:
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 λ has an inverse relationship to frequency f, 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, dealing with signals (waves) in air we have the speed of sound in air, so the conversion becomes,
\lambda = \frac{c}{f}
where:
- λ = wavelength of an electromagnetic wave or
- λ = wavelength of a sound wave
- c = speed of light in vacuum = 299,792.458 km/s ~ 300,000 km/s = 300,000,000 m/s or
- c = speed of sound in air = 343 m/s at 20 °C (68 °F)
- f = 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:
\lambda^\prime = \frac{\lambda_0}{n}
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
\lambda = \frac{h}{p} = \frac {h}{mv} \sqrt{1 - \frac{v^2}{c^2}}
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.
See also: frequency, period, amplitude
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