- Wavelength
In

physics **wavelength**is the distance between repeating units of a propagatingwave of a givenfrequency . It is commonly designated by the Greek letter "lambda " (λ). Examples of wave-like phenomena arelight ,water wave s, andsound wave s. The wavelength is related to the frequency by the formula:wavelength = wave speed / frequency.Wavelength is therefore inversely proportional to frequency. Higher frequencies have shorter wavelengths. Lower frequencies have longer wavelengths, assuming the speed of the wave is the same.In a wave, properties vary with position. For example, in a

sound wave the air pressure oscillates, while inlight and otherelectromagnetic radiation the strength of the electric and themagnetic field vary.Visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm (430–750 THz). For other examples, see

electromagnetic spectrum . The wavelengths of sound frequencies audible to the human ear (20 Hz–20 kHz) are between approximately 17 m and 17 mm, respectively; the wavelengths in audible sound are much longer than those in visible light.**Relationship with frequency**Wavelength "λ" is determined using the formula

:$lambda\; =\; frac\{v\}\{f\}$

Where "v" is the

propagation speed of the wave and "f" is its frequency. In the case ofelectromagnetic radiation , such as light, in a vacuum, this velocity is thespeed of light , 299,792,458 m/s or about 3×10^{8}m/s. Forsound wave s in air, this is thespeed of sound , 345 m/s (1238 km/h) in air at room temperature and atmospheric pressure. Usually,SI units are used, where the wavelength is expressed inmetre s, the frequency in Hz, and the propagation velocity in metres persecond .For example, the wavelength for a 100 MHz electromagnetic (radio) wave is about: "λ" = 3×10

^{8}m/s divided by 100×10^{6}Hz = 3 metres. Electronic engineers often use a shortcut formula: wavelength "λ" in metres = 300 Mm/s divided by the frequency in MHz, to avoid counting the (many) zero digits in the decimal orscientific notation s.It should be noted that for many wave phenomena, wavelength is not the distance that particles travel during a period. For instance, in

acoustics andwater waves , the particle displacements during a period are only a small fraction of the wavelength, apart from extreme conditions likebreaking wave s andshock wave s.It should also be noted that frequency and wavelength can change independently, but only when the speed of the wave changes. For example, when light enters another medium, its speed and wavelength change while its frequency does not.

**In non-vacuum media**The speed of light in most media is lower than in vacuum, which means that the same frequency will correspond to a shorter wavelength in the medium than in vacuum. The wavelength in the medium is:$lambda\text{'}=frac\{lambda\_0\}\{n\}$ where "n" is the

refractive index of the medium. Wavelengths of electromagnetic radiation are usually quoted in terms of the vacuum wavelength, unless specifically indicated as the "wavelength in the medium". In acoustics, where a medium is essential for the waves to exist, the term wavelength is always the wavelength in the medium. Then the refractive index depends on the mean properties of the medium, for instance the mean pressure or changes in the material composition.**De Broglie wavelength of particles**Louis de Broglie postulated that all particles withmomentum have a wavelength:$lambda\; =\; frac\{h\}\{p\}$where "h" isPlanck's constant , and "p" is themomentum of the particle. This hypothesis was at the basis ofquantum mechanics . Nowadays, this wavelength is called thede Broglie wavelength . For example, theelectron s in a CRT display have a De Broglie wavelength of about 10^{-13}m."'**ee also***

Amplitude

*Angular frequency

*Frequency

*Fraunhofer lines , spectral lines traditionally used as standard optical wavelength references

*Periodic function

*Wave vector **External links*** [

*http://www.sengpielaudio.com/calculator-wavelength.htm Conversion: Wavelength to Frequency and vice versa - Sound waves and radio waves*]

* [*http://www.acoustics.salford.ac.uk/schools/index1.htm Teaching resource for 14-16yrs on sound including wavelength*]

* [*http://www.magnetkern.de/spektrum.html The visible electromagnetic spectrum displayed in web colors with according wavelengths*]

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