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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 plane wave ： ウィキペディア英語版 plane wave In the physics of wave propagation, a plane wave (also spelled planewave) is a constant-frequency wave whose wavefronts (surfaces of constant phase) are infinite parallel planes of constant peak-to-peak amplitude normal to the phase velocity vector. It is not possible in practice to have a true plane wave; only a plane wave of infinite extent will propagate as a plane wave. However, many waves are approximately plane waves in a localized region of space. For example, a localized source such as an antenna produces a field that is approximately a plane wave far from the antenna in its far-field region. Similarly, if the length scales are much longer than the wave’s wavelength, as is often the case for light in the field of optics, one can treat the waves as light rays which correspond locally to plane waves. == Mathematical formalisms == Two functions that meet the above criteria of having a constant frequency and constant amplitude are the sine and cosine functions. One of the simplest ways to use such a sinusoid involves defining it along the direction of the x-axis. The equation below, which is illustrated toward the right, uses the cosine function to represent a plane wave travelling in the positive x direction. :$A(x,t)=A\_o\; \backslash cos\; (k\; x\; -\; \backslash omega\; t+\backslash varphi)$ In the above equation: * $A(x,t)\backslash ,$ is the magnitude or disturbance of the wave at a given point in space and time. An example would be to let $A(x,t)\backslash ,$ represent the variation of air pressure relative to the norm in the case of a sound wave. * $A\_o\backslash ,$ is the amplitude of the wave which is the peak magnitude of the oscillation. * $k\backslash ,$ is the wave’s wave number or more specifically the ''angular'' wave number and equals , where is the wavelength of the wave. $k\backslash ,$ has the units of radians per unit distance and is a measure of how rapidly the disturbance changes over a given distance at a particular point in time. * $x\backslash ,$ is a point along the x-axis. $y\backslash ,$ and $z\backslash ,$ are not part of the equation because the wave's magnitude and phase are the same at every point on any given plane. This equation defines what that magnitude and phase are. * $\backslash omega\backslash ,$ is the wave’s angular frequency which equals , where is the period of the wave. $\backslash omega\backslash ,$ has the units of radians per unit time and is a measure of how rapidly the disturbance changes over a given length of time at a particular point in space. * $t\backslash ,$ is a given point in time * $\backslash varphi\; \backslash ,$ is the phase shift of the wave and has the units of radians. Note that a positive phase shift, at a given moment of time, shifts the wave in the negative x-axis direction. A phase shift of radians shifts it exactly one wavelength. Other formalisms which directly use the wave’s wavelength $\backslash lambda\backslash ,$, period $T\backslash ,$, frequency $f\backslash ,$ and velocity $c\backslash ,$ are below. :$A=A\_o\; \backslash cos(t/T)\; +\; \backslash varphi)\backslash ,$ :$A=A\_o\; \backslash cos(ft)\; +\; \backslash varphi)\backslash ,$ :$A=A\_o\; \backslash cos(ct)\; +\; \backslash varphi)\backslash ,$ To appreciate the equivalence of the above set of equations note that $f=1/T\backslash ,\backslash !$ and $c=\backslash lambda/T=\backslash omega/k\backslash ,\backslash !$ 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「plane wave」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.