Wavelength

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 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,

where:

λ = wavelength of an electromagnetic wave
c = speed of light = 299,792.458 km/s ~ 300,000 km/s = 300,000,000 m/s or
c = speed in air = 343 m/s at 20 ÃÂÃÂ°C (68 ÃÂÃÂ°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:

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.

Weblink

Conversion: Wavelength to Frequency and back

Wavelength is the title of a 1978 album by Van Morrison.