## Wavelength |

In **wavelength** is the **spatial period** of a periodic wave—the distance over which the wave's shape repeats.^{[1]}^{[2]} It is thus the ^{[3]}^{[4]} Wavelength is commonly designated by the * lambda* (λ). The term

Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to ^{[6]}

Wavelength depends on the medium (for example, vacuum, air, or water) that a wave travels through.

Examples of wave-like phenomena are

Wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in sinusoidal waves over deep water a particle near the water's surface moves in a circle of the same diameter as the wave height, unrelated to wavelength.^{[7]} The range of wavelengths or frequencies for wave phenomena is called a

- sinusoidal waves
- more general waveforms
- interference and diffraction
- subwavelength
- angular wavelength
- see also
- references
- external links

In *λ* of a sinusoidal waveform traveling at constant speed *v* is given by^{[8]}

where *v* is called the phase speed (magnitude of the *f* is the wave's

In the case of ^{8} m/s. Thus the wavelength of a 100 MHz electromagnetic (radio) wave is about: 3×10^{8} m/s divided by 10^{8} Hz = 3 metres. The wavelength of visible light ranges from deep

For

A

The upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box (an example of

The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities.^{[9]} Consequently, wavelength, period, and wave velocity are related just as for a traveling wave. For example, the

Traveling sinusoidal waves are often represented mathematically in terms of their velocity *v* (in the x direction), frequency *f* and wavelength *λ* as:

where *y* is the value of the wave at any position *x* and time *t*, and *A* is the *k* (2π times the reciprocal of wavelength) and *ω* (2π times the frequency) as:

in which wavelength and wavenumber are related to velocity and frequency as:

or

In the second form given above, the phase (*kx* − *ωt*) is often generalized to (**k**•**r** − *ωt*), by replacing the wavenumber *k* with a **r**. In that case, the wavenumber *k*, the magnitude of **k**, is still in the same relationship with wavelength as shown above, with *v* being interpreted as scalar speed in the direction of the wave vector. The first form, using reciprocal wavelength in the phase, does not generalize as easily to a wave in an arbitrary direction.

Generalizations to sinusoids of other phases, and to complex exponentials, are also common; see

The speed of a wave depends upon the medium in which it propagates. In particular, the speed of light in a medium is less than in

This change in speed upon entering a medium causes ^{[10]} For

The wave velocity in one medium not only may differ from that in another, but the velocity typically varies with wavelength. As a result, the change in direction upon entering a different medium changes with the wavelength of the wave.

For electromagnetic waves the speed in a medium is governed by its * refractive index* according to

where *c* is the *n*(λ_{0}) is the refractive index of the medium at wavelength λ_{0}, where the latter is measured in vacuum rather than in the medium. The corresponding wavelength in the medium is

When wavelengths of electromagnetic radiation are quoted, the wavelength in vacuum usually is intended unless the wavelength is specifically identified as the wavelength in some other medium. In acoustics, where a medium is essential for the waves to exist, the wavelength value is given for a specified medium.

The variation in speed of light with vacuum wavelength is known as

Wavelength can be a useful concept even if the wave is not *local* wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with the local water depth.^{[11]}

Waves that are sinusoidal in time but propagate through a medium whose properties vary with position (an *inhomogeneous* medium) may propagate at a velocity that varies with position, and as a result may not be sinusoidal in space. The figure at right shows an example. As the wave slows down, the wavelength gets shorter and the amplitude increases; after a place of maximum response, the short wavelength is associated with a high loss and the wave dies out.

The analysis of * WKB method* (also known as the

Waves in crystalline solids are not continuous, because they are composed of vibrations of discrete particles arranged in a regular lattice. This produces ^{[14]} Descriptions using more than one of these wavelengths are redundant; it is conventional to choose the longest wavelength that fits the phenomenon. The range of wavelengths sufficient to provide a description of all possible waves in a crystalline medium corresponds to the wave vectors confined to the ^{[15]}

This indeterminacy in wavelength in solids is important in the analysis of wave phenomena such as

Other Languages

Afrikaans: Golflengte

العربية: طول الموجة

asturianu: Llonxitú d'onda

azərbaycanca: Dalğa uzunluğu

تۆرکجه: دالغا بویو

বাংলা: তরঙ্গ দৈর্ঘ্য

Bân-lâm-gú: Pho-tn̂g

беларуская: Даўжыня хвалі

беларуская (тарашкевіца): Даўжыня хвалі

български: Дължина на вълната

Boarisch: Wöönläng

bosanski: Talasna dužina

brezhoneg: Hirder gwagenn

català: Longitud d'ona

čeština: Vlnová délka

Cymraeg: Tonfedd

dansk: Bølgelængde

Deutsch: Wellenlänge

eesti: Lainepikkus

Ελληνικά: Μήκος κύματος

español: Longitud de onda

Esperanto: Ondolongo

euskara: Uhin-luzera

فارسی: طول موج

français: Longueur d'onde

Frysk: Weachlingte

Gaeilge: Tonnfhad

Gàidhlig: Tonn-fhad

galego: Lonxitude de onda

ગુજરાતી: તરંગલંબાઈ

한국어: 파장

հայերեն: Ալիքի երկարություն

हिन्दी: तरंगदैर्घ्य

hrvatski: Valna duljina

Bahasa Indonesia: Panjang gelombang

íslenska: Bylgjulengd

italiano: Lunghezza d'onda

עברית: אורך גל

ქართული: ტალღის სიგრძე

қазақша: Толқын ұзындығы

Kiswahili: Masafa ya mawimbi

Kreyòl ayisyen: Longèdonn

kurdî: Pêldirêjahî

Latina: Longitudo undae

latviešu: Viļņa garums

Lëtzebuergesch: Wellelängt

lietuvių: Bangos ilgis

magyar: Hullámhossz

македонски: Бранова должина

മലയാളം: തരംഗദൈർഘ്യം

मराठी: तरंगलांबी

Bahasa Melayu: Panjang gelombang

Nederlands: Golflengte

日本語: 波長

Nordfriisk: Waagenlengde

norsk: Bølgelengde

norsk nynorsk: Bølgjelengd

occitan: Longor d'onda

ଓଡ଼ିଆ: ତରଙ୍ଗ ଦୈର୍ଘ୍ୟ

oʻzbekcha/ўзбекча: Toʻlqin uzunligi

ਪੰਜਾਬੀ: ਛੱਲ-ਲੰਬਾਈ

پنجابی: ویو لینتھ

پښتو: څپواټن

Plattdüütsch: Bülgenläng

polski: Długość fali

português: Comprimento de onda

română: Lungime de undă

русиньскый: Вовнова довжка

русский: Длина волны

Scots: Swawlenth

shqip: Gjatësia e valës

සිංහල: තරංග ආයාමය

Simple English: Wavelength

slovenčina: Vlnová dĺžka

slovenščina: Valovna dolžina

Soomaaliga: Dhererka Mowjadda

کوردی: درێژیی شەپۆل

српски / srpski: Таласна дужина

srpskohrvatski / српскохрватски: Talasna dužina

suomi: Aallonpituus

svenska: Våglängd

Tagalog: Alonghaba

தமிழ்: அலைநீளம்

татарча/tatarça: Дулкын озынлыгы

తెలుగు: తరంగ దైర్ఘ్యం

ไทย: ความยาวคลื่น

тоҷикӣ: Адади мавҷӣ

Türkçe: Dalga boyu

українська: Довжина хвилі

اردو: طولِ موج

Tiếng Việt: Bước sóng

粵語: 波長

中文: 波长