Phase velocity refers to the phase velocity orphaseSpeed, or phase speed for short, is defined as the advancing speed of the constant phase point of the electromagnetic wave.In other words, the phase of any frequency component of the wave is transmitted at this speed.Any specific phase of the wave can be selected for observation (such as wave crest), and then it will move forward at the phase speed.
Chinese name
Phase velocity
Foreign name
Phase velocity
Formula
Vp=fλ=ω/β
Abbreviation
Phase velocity
Concept
The constant phase of wave propagation velocity in space
。Here β is the phase constant, and the subscript p is
Phase velocity.The phase velocity can be frequency dependent or frequency independent, depending on the phase constant β.In an ideal medium,
And angular frequency
Is linear, so
Is a constant independent of frequency, so the ideal medium isdispersionOf.However, in dispersive media (such as conductive media), the phase constant β no longer corresponds to the angular frequency
The phase velocity of electromagnetic wave changes with frequency, resulting in dispersion.[1]
Phase velocity group velocity
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When a radio wave propagates in a medium, if the dielectric constant ε of the medium is independent of frequency, the propagation speed of the wave is also independent of frequency. This medium is calledNondispersive medium；On the contrary, if ε or propagation velocity v of the medium is related to frequency, it is called dispersive medium.
The formula for the propagation velocity of monochromatic waves is derived from the propagation of the isophase surface, so it is called the phase velocity.
Phase velocity: sine of single frequencyelectromagnetic waveThe velocity of wave's isophase surface (such as wave crest or wave trough) propagating in the medium v=c/n, and c is freespaceInlight speed, n is the refractive index of the medium to the electromagnetic wave of this frequency.
The signal of a practical system is always composed of many frequency componentsdispersionIn the medium, each monochromatic component will propagate at different phase velocities, so it is difficult to determine the propagation velocity of the signal in the dispersive medium. Therefore, the concept of group velocity is introduced, which describes the energy propagation velocity of the signal.aboutthe ionosphere（Earth's atmosphereFrom bottom to top, it is divided into tropospherestratosphereIonosphereMagnetosphere）Because the refractive index n ＜ 1, the phase velocity of radio waves is greater than the speed of light c. This conclusion is not contradictory to the theory of relativity, because the phase velocity only representsphaseThe speed of change does not represent the true propagation speed of electromagnetic wave energy.The group velocity is always less than the speed of light c in free space.
group velocityThe propagation speed of the composite signal of many different frequency sine electromagnetic waves in the medium.The amplitude and phase of sine waves with different frequencies are different. In dispersive media, the phase velocity is different, sospatial location The shape of the composite signal on the changes.Group velocity is the advancing velocity of any constant phase point on the envelope wave, which represents the propagation velocity of energy.
situation analysis
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Analysis of the relationship between group velocity and phase velocity and dispersion
The relationship between group velocity and phase velocity and dispersion analysis can be referred togroup velocity。
