Phase velocity

Japanese: 位相速度 - いそうそくど（英語表記）phase velocity

One of the wave velocities. It is the speed at which a wave travels in a direction perpendicular to the plane formed by connecting points in the same phase in a medium, i.e., the wave front. It is often used to distinguish it from the group velocity of wave motion. A sine wave traveling in the positive direction of the x- axis is expressed as ξ = a sin (ω t - kx + ε), and the phase velocity v is given by v = ω/ k = λ/ T. Here, a is the amplitude of the wave, ω is the angular frequency, k is the wave number, ε is the initial phase, λ is the wavelength, and T is the period. Strictly speaking, phase velocity is defined for sine waves. However, even if several sine waves with different frequencies but the same phase velocity travel through an isotropic medium, the composite wave (wave packet) will have this phase velocity. In this case, it is called there is no dispersion, and it occurs when the angular frequency ω is proportional to the wave number. In contrast, when the phase velocities of each sine wave are different, the speed at which the composite wave travels without breaking down is the group velocity. Therefore, if there is no dispersion, the phase velocity and the group velocity are equal. When we talk about speed, we usually mean phase velocity. (→Wave speed)

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

波の速度の1つ。媒質中で同じ位相にある点を結んでつくられる面，すなわち波面に垂直な方向に進む速さ。波動の群速度と区別するときによく用いられる。 x 軸の正の向きに進む正弦波は ξ＝a sin (ωt－kx＋ε) で表わされ，位相速度 v は v＝ω/k＝λ/T で与えられる。ただし a は波の振幅，ω は角振動数，k は波数，ε は初位相，λ は波長，T は周期を示す。位相速度は厳密にいうと正弦波について定義される。しかし，等方性の媒質中を，振動数は異なるが位相速度が等しいいくつかの正弦波が進行する場合でも，合成波 (波束 ) はこの位相速度をもつ。このとき分散がないと呼び，角振動数ωが波数に比例するときに起る。これに対して，各正弦波の位相速度が異なるとき，合成波がくずれずに進む速さが群速度である。したがって分散がなければ位相速度と群速度は等しい。波を扱うとき速度といえば，普通は位相速度をさす。 (→波の速度 )

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