Таласна дужина — разлика између измена

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{{Short description|Просторни период таласа — раздаљина на којој се облик таласа понавља, а тиме и инверзна просторна фреквенција}}{{рут}}
[[Датотека:talas.png|десно|400п|мини|Објашњење таласне дужине]]
[[Датотека:Sine wavelength.svg|thumb|right|250п|The wavelength of a [[sine wave]], λ, can be measured between any two points with the same [[phase (waves)|phase]], such as between crests (on top), or troughs (on bottom), or corresponding [[zero crossing]]s as shown.]]
'''Таласна дужина''' је карактеристика сваког [[Талас|таласа]], као и [[фреквенција]]. Сваки талас има и своју амплитуду која означава интензитет таласа.
[[Датотека:talas.png|десно|250п|мини|Објашњење таласне дужине]]
 
'''Таласна дужина''' је карактеристика сваког [[Талас|таласа]], као и [[фреквенција]]. Сваки талас има и своју амплитуду која означава интензитет таласа. Путовање таласа описује [[синус]]на функција, а таласна дужина код трансверзалних таласа је дужина између два суседна врха таласа (или два удубљења). Мерна јединица за таласну дужину у Међународном систему јединица [[Основне јединице СИ система|СИ]] је [[метар]]. Таласна дужина је такође и најкраћа раздаљина између две [[Čestice|честице]] које осцилују у истој фази. Таласна дужина означава се са грчким словом ''lambda'' - <math>\lambda</math>
 
In [[physics]], the '''wavelength''' is the '''spatial period''' of a periodic wave—the distance over which the wave's shape repeats.<ref name=hecht>
Таласна дужина је такође и најкраћа раздаљина између две [[Čestice|честице]] које осцилују у истој фази.
{{cite book
|first=Eugene
|last=Hecht
|year=1987
|title=Optics
|edition=2nd
|publisher=Addison Wesley
|isbn=0-201-11609-X
|pages=15–16
}}</ref><ref name=Flowers>
{{cite book
|title=An introduction to numerical methods in C++
|chapter=§21.2 Periodic functions
|page=473
|chapter-url=https://books.google.com/books?id=weYj75E_t6MC&pg=RA1-PA473
|author=Brian Hilton Flowers
|isbn=0-19-850693-7
|year=2000
|edition=2nd
|publisher = Cambridge University Press
}}</ref> It is the distance between consecutive corresponding points of the same [[phase (waves)|phase]] on the wave, such as two adjacent crests, troughs, or [[zero crossing]]s, and is a characteristic of both traveling waves and [[standing wave]]s, as well as other spatial wave patterns.<ref name=Seaway>
{{cite book
|title=Principles of physics
|author1=Raymond A. Serway |author2=John W. Jewett |pages=404, 440
|url=https://books.google.com/books?id=1DZz341Pp50C&pg=PA404
|edition=4th
|isbn=0-534-49143-X
|publisher=Cengage Learning
|year=2006 }}</ref><ref>
{{cite book
| title=The surface physics of liquid crystals
| author=A. A. Sonin
| publisher=Taylor & Francis
| year=1995
| isbn=2-88124-995-7
| page=17
}}</ref> The [[multiplicative inverse|inverse]] of the wavelength is called the [[spatial frequency]]. Wavelength is commonly designated by the [[Greek letter]] ''[[lambda]]'' (λ).
The term ''wavelength'' is also sometimes applied to [[modulation|modulated]] waves, and to the sinusoidal [[envelope (mathematics)|envelopes]] of modulated waves or waves formed by [[Interference (wave propagation)|interference]] of several sinusoids.<ref>
{{cite book
| title = Electromagnetic Theory for Microwaves and Optoelectronics
|author1=Keqian Zhang |author2=Dejie Li
| publisher = Springer
| year = 2007
| isbn = 978-3-540-74295-1
| page = 533
| url = https://books.google.com/books?id=3Da7MvRZTlAC&q=wavelength+modulated-wave+envelope&pg=PA533
}}</ref>
 
Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to [[frequency]] of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.<ref>
Таласна дужина означава се са грчким словом ''lambda'' - <math>\lambda</math>
{{cite book
| title = In Quest of the Universe
|author1=Theo Koupelis |author2=Karl F. Kuhn
| publisher = Jones & Bartlett Publishers
| year = 2007
| isbn = 978-0-7637-4387-1
| url = https://archive.org/details/inquestofunivers00koup | url-access = registration
| page = [https://archive.org/details/inquestofunivers00koup/page/102 102]
| quote = wavelength lambda light sound frequency wave speed.
}}</ref>
 
Wavelength depends on the medium (for example, vacuum, air, or water) that a wave travels through. Examples of waves are [[sound wave]]s, [[light]], [[water wave]]s and periodic electrical signals in a [[Electrical conductor|conductor]]. A [[sound]] wave is a variation in air [[sound pressure|pressure]], while in [[light]] and other [[electromagnetic radiation]] the strength of the [[electric field|electric]] and the [[magnetic field]] vary. Water waves are variations in the height of a body of water. In a crystal [[lattice vibration]], atomic positions vary.
 
The range of wavelengths or frequencies for wave phenomena is called a [[spectrum]]. The name originated with the [[Visible spectrum|visible light spectrum]] but now can be applied to the entire [[electromagnetic spectrum]] as well as to a [[sound spectrum]] or [[vibration spectrum]].
 
==Sinusoidal waves==
In [[linear]] media, any wave pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength ''λ'' of a sinusoidal waveform traveling at constant speed ''v'' is given by<ref name= Cassidy>
{{cite book
|title=Understanding physics
|author1=David C. Cassidy |author2=Gerald James Holton |author3=Floyd James Rutherford |url=https://books.google.com/books?id=rpQo7f9F1xUC&pg=PA340
|pages=339 ''ff''
|isbn=0-387-98756-8
|year=2002
|publisher=Birkhäuser}}
</ref>
 
:<math>\lambda = \frac{v}{f}\,\,,</math>
 
where ''v'' is called the phase speed (magnitude of the [[phase velocity]]) of the wave and ''f'' is the wave's [[frequency]]. In a [[dispersive medium]], the phase speed itself depends upon the frequency of the wave, making the [[dispersion relation|relationship between wavelength and frequency]] nonlinear.
 
In the case of [[electromagnetic radiation]]—such as light—in [[free space]], the phase speed is the [[speed of light]], about 3×10<sup>8</sup>&nbsp;m/s. Thus the wavelength of a 100&nbsp;MHz electromagnetic (radio) wave is about: 3×10<sup>8</sup>&nbsp;m/s divided by 10<sup>8</sup>&nbsp;Hz = 3 metres. The wavelength of visible light ranges from deep [[red]], roughly 700 [[nanometre|nm]], to [[Violet (color)|violet]], roughly 400&nbsp;nm (for other examples, see [[electromagnetic spectrum]]).
 
For [[sound wave]]s in air, the [[speed of sound]] is 343&nbsp;m/s (at [[standard conditions for temperature and pressure|room temperature and atmospheric pressure]]). The wavelengths of sound frequencies audible to the human ear (20&nbsp;[[hertz|Hz]]–20&nbsp;kHz) are thus between approximately 17&nbsp;[[metre|m]] and 17&nbsp;[[millimetre|mm]], respectively. Somewhat higher frequencies are used by [[bat]]s so they can resolve targets smaller than 17&nbsp;mm. Wavelengths in audible sound are much longer than those in visible light.
 
[[File:Waves in Box.svg|thumb|Sinusoidal standing waves in a box that constrains the end points to be nodes will have an integer number of half wavelengths fitting in the box.]]
[[File:Standing wave 2.gif|thumb|right|A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue)]]
 
===Standing waves===
A [[standing wave]] is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called [[node (physics)|nodes]], and the wavelength is twice the distance between nodes.
 
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 [[boundary conditions]]) determining which wavelengths are allowed. For example, for an electromagnetic wave, if the box has ideal metal walls, the condition for nodes at the walls results because the metal walls cannot support a tangential electric field, forcing the wave to have zero amplitude at the wall.
 
The stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities.<ref>{{cite book
| title = The World of Physics
| author = John Avison
| publisher = Nelson Thornes
| year = 1999
| isbn = 978-0-17-438733-6
| page = 460
| url = https://books.google.com/books?id=DojwZzKAvN8C&q=%22standing+wave%22+wavelength&pg=PA460
}}</ref> Consequently, wavelength, period, and wave velocity are related just as for a traveling wave. For example, the [[Speed of light#Cavity resonance|speed of light]] can be determined from observation of standing waves in a metal box containing an ideal vacuum.
 
===Mathematical representation===
Traveling sinusoidal waves are often represented mathematically in terms of their velocity ''v'' (in the x direction), frequency ''f'' and wavelength ''λ'' as:
 
:<math> y (x, \ t) = A \cos \left( 2 \pi \left( \frac{x}{\lambda } - ft \right ) \right ) = A \cos \left( \frac{2 \pi}{\lambda} (x - vt) \right )</math>
 
where ''y'' is the value of the wave at any position ''x'' and time ''t'', and ''A'' is the [[amplitude]] of the wave. They are also commonly expressed in terms of [[wavenumber]] ''k'' (2π times the reciprocal of wavelength) and [[angular frequency]] ''ω'' (2π times the frequency) as:
 
:<math> y (x, \ t) = A \cos \left( kx - \omega t \right) = A \cos \left(k(x - v t) \right) </math>
 
in which wavelength and wavenumber are related to velocity and frequency as:
 
:<math> k = \frac{2 \pi}{\lambda} = \frac{2 \pi f}{v} = \frac{\omega}{v},</math>
 
or
 
:<math> \lambda = \frac{2 \pi}{k} = \frac{2 \pi v}{\omega} = \frac{v}{f}.</math>
 
In the second form given above, the phase {{nowrap|(''kx'' − ''ωt'')}} is often generalized to {{nowrap|('''k'''•'''r''' − ''ωt'')}}, by replacing the wavenumber ''k'' with a [[wave vector]] that specifies the direction and wavenumber of a [[plane wave]] in [[3-space]], parameterized by position vector '''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 [[plane wave]]. The typical convention of using the [[cosine]] phase instead of the [[sine]] phase when describing a wave is based on the fact that the cosine is the real part of the complex exponential in the wave
:<math>A e^{ i \left( kx - \omega t \right)}. </math>
 
== Види још ==
* [[Таласна једначина]]
* [[Електромагнетски спектар|Електромагнетни спектар]]
* [[Спектар]]
 
== Референце ==
{{Reflist|}}
 
== Литература ==
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{{refend}}
 
== Спољашње везе ==
{{commons category|Wavelength}}
* [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 14–16 years 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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[[Категорија:Таласи]]