Definitions for phase velocity
phase veloc·i·ty

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1. phase velocitynoun

   the velocity of propagation of a pure sine wave of infinite extent and infinitesimal amplitude

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1. Phase velocity

   The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and time period T as v p = λ T . {\displaystyle v_{\mathrm {p} }={\frac {\lambda }{T}}.} Equivalently, in terms of the wave's angular frequency ω, which specifies angular change per unit of time, and wavenumber (or angular wave number) k, which represent the angular change per unit of space, v p = ω k . {\displaystyle v_{\mathrm {p} }={\frac {\omega }{k}}.} To gain some basic intuition for this equation, we consider a propagating (cosine) wave A cos(kx − ωt). We want to see how fast a particular phase of the wave travels. For example, we can choose kx - ωt = 0, the phase of the first crest. This implies kx = ωt, and so v = x / t = ω / k. Formally, we let the phase φ = kx - ωt and see immediately that ω = -dφ / dt and k = dφ / dx. So, it immediately follows that ∂ x ∂ t = − ∂ ϕ ∂ t ∂ x ∂ ϕ = ω k . {\displaystyle {\frac {\partial x}{\partial t}}=-{\frac {\partial \phi }{\partial t}}{\frac {\partial x}{\partial \phi }}={\frac {\omega }{k}}.} As a result we observe a inverse relation between the angular frequency and wavevector. If the wave has higher frequency oscillations, the wave length must be shortened for the phase velocity to remain constant. Additionally, the phase velocity of electromagnetic radiation may – under certain circumstances (for example anomalous dispersion) – exceed the speed of light in vacuum, but this does not indicate any superluminal information or energy transfer. It was theoretically described by physicists such as Arnold Sommerfeld and Léon Brillouin.

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1. Phase velocity

   The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ and period T as Or, equivalently, in terms of the wave's angular frequency ω, which specifies the number of oscillations per unit of time, and wavenumber k, which specifies the number of oscillations per unit of space, by To understand where this equation comes from, imagine a basic sine wave, A cos . Given time t, the source produces ωt oscillations. At the same time, the initial wave front propagates away from the source through the space to the distance x to fit the same amount of oscillations, kx = ωt. So that the propagation velocity v is v = x/t = ω/k. The wave propagates faster when higher frequency oscillations are distributed less densely in space. Formally, Φ = kx−ωt is the phase. Since ω = −dΦ/dt and k = +dΦ/dx, the wave velocity is v = dx/dt = ω/k.

How to pronounce phase velocity?

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Numerology

1. Chaldean Numerology

   The numerical value of phase velocity in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of phase velocity in Pythagorean Numerology is: 7

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Phase_Velocity
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Phase_Velocity
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=phase velocity