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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Dispersion relation ： ウィキペディア英語版 Dispersion relation In physical sciences and electrical engineering, dispersion relations describe the effect of dispersion in a medium on the properties of a wave traveling within that medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. From this relation the phase velocity and group velocity of the wave have convenient expressions which then determine the refractive index of the medium. More general than the geometry-dependent and material-dependent dispersion relations, there are the overarching Kramers–Kronig relations that describe the frequency dependence of wave propagation and attenuation. Dispersion may be caused either by geometric boundary conditions (waveguides, shallow water) or by interaction of the waves with the transmitting medium. Elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media. In the presence of dispersion, wave velocity is no longer uniquely defined, giving rise to the distinction of phase velocity and group velocity. ==Dispersion== Dispersion occurs when pure plane waves of different wavelengths have different propagation velocities, so that a wave packet of mixed wavelengths tends to spread out in space. The speed of a plane wave, ''v'', is a function of the wave's wavelength $\backslash lambda$: :$v\; =\; v(\backslash lambda).\backslash ,$ The wave's speed, wavelength, and frequency, ''f'', are related by the identity :$v(\backslash lambda)\; =\; \backslash lambda\backslash \; f(\backslash lambda).\backslash ,$ The function ''f''(''λ'') expresses the dispersion relation of the given medium. Dispersion relations are more commonly expressed in terms of the angular frequency $\backslash omega=2\backslash pi\; f$ and wavenumber $k=2\; \backslash pi\; /\backslash lambda$. Rewriting the relation above in these variables gives :$\backslash omega(k)=\; v(k)\backslash \; k.\backslash ,$ where we now view ''f'' as a function of ''k''. The use of ω(''k'') to describe the dispersion relation has become standard because both the phase velocity ω/''k'' and the group velocity dω/d''k'' have convenient representations via this function. The plane waves being considered can be described by :$A(x,\; t)\; =\; A\_0e^\}=\; A\_0e^,$ where :''A'' is the amplitude of the wave, :''A''0 = ''A''(0,0), :''x'' is a position along the wave's direction of travel, and :''t'' is the time at which the wave is described. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dispersion relation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.