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Encyclopedia > Wavelengths

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, for signals (waves) in air, this is the speed of sound in air. The relationship is given by:

where:

λ = wavelength of a sound wave or electromagnetic 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 approximated with the formula: wavelength (in metres) = 300 / frequency (in megahertz).


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 but the frequey 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, no matter what medium they are travelling through, are uslly 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 Planck's constant
p is the particle's momentum
m is the particle's mass
v is the particle's velocity

The greater the energy, the larger the frequency and the shorter (smaller) the wavelength. Given te relationship between wavelength and frequency, it follows that short wavelengths are more energetic than long wavelengths.


See Also

Waves


frequency, period, amplitude


External link

  • Conversion: Wavelength to Frequency and back (http://www.sengpielaudio.com/calculator-wavelength.htm)


  Results from FactBites:
 
Frequency Wavelength Calculator (846 words)
The relationship between a radio signal's frequency and its wavelength can be found by the industry accepted formula wavelength equals 300 divided by the frequency in megahertz.
Assuming the formula is correct, a frequency of 27185 kHz would be equivalent to a wavelength of 11.035 meters (try it on the calculator but be sure to click on Full Wave...), which we would round to 11 meters.
This is important because the length or height of various types of antennas must often be a fraction (usually one-quarter or one-half) of the wavelength of the signal to be transmitted or received.
  More results at FactBites »

 
 

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