Phase velocity
Speed of a wave's constant-phase surface.
Phase velocity is the speed at which a wavefront, or surface of constant phase, travels. For a constant-frequency component of a wave, any given phase, such as a crest, appears to move at this velocity. It is defined for sinusoidal waves as the ratio of wavelength to time period, or equivalently as angular frequency divided by wavenumber.
- definition
- Speed of a wavefront, surface of constant phase
- formula_sinusoidal
- v_p = λ / T
- formula_angular
- v_p = ω / k
- relation_to_refractive_index
- n = c / v_p = ck / ω
- non_dispersive_condition
- ∂n/∂ω = 0
- group_velocity_formula
- v_g = c / (n + ω ∂n/∂ω)
Lore & Background
The phase velocity of a wave is the speed of any wavefront, a surface of constant phase. This is the velocity at which the phase of any constant-frequency component of the wave travels. For such a spectral component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity of light waves is not a physically meaningful quantity and is not related to information transfer.
Reader's Guide
Phase velocity is a fundamental concept in wave physics, describing the speed of a wave's phase fronts. For a simple sinusoidal wave, it is given by v_p = λ / T or v_p = ω / k. The definition extends to beats or signals composed of multiple waves, where the phase velocity of the carrier determines the phase velocity of the wave set. In electromagnetics and optics, the frequency is a function of wavenumber, so phase velocity and group velocity depend on the medium and frequency. The refractive index is defined as n = c / v_p. Group velocity equals phase velocity only when the refractive index is independent of frequency (non-dispersive medium). The relation ω(k) is known as the dispersion relation of the medium.
Did You Know?
- Phase velocity is the speed of any wavefront, a surface of constant phase.
- For a simple sinusoidal wave, phase velocity equals wavelength divided by time period.
- The phase velocity of light waves is not a physically meaningful quantity and is not related to information transfer.
- Group velocity equals phase velocity only when the refractive index is independent of frequency.
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