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is the speed of light (i.e. phase velocity) in a medium with permeability μ, and permittivity ε, and ∇ 2 is the Laplace operator. In a vacuum, v ph = c 0 = 299 792 458 m/s, a fundamental physical constant. [1] The electromagnetic wave equation derives from Maxwell's equations.
where v is the speed of the wave (c in a vacuum or less in other media), f is the frequency and λ is the wavelength. As waves cross boundaries between different media, their speeds change but their frequencies remain constant. Electromagnetic waves in free space must be solutions of Maxwell's electromagnetic wave equation. Two main classes of ...
Maxwell's equations may be combined to demonstrate how fluctuations in electromagnetic fields (waves) propagate at a constant speed in vacuum, c (299 792 458 m/s [2]). Known as electromagnetic radiation, these waves occur at various wavelengths to produce a spectrum of radiation from radio waves to gamma rays.
Sometimes c is used for the speed of waves in any material medium, and c 0 for the speed of light in vacuum. [12] This subscripted notation, which is endorsed in official SI literature, [ 13 ] has the same form as related electromagnetic constants: namely, μ 0 for the vacuum permeability or magnetic constant, ε 0 for the vacuum permittivity ...
For electromagnetic waves in vacuum, the angular frequency is proportional to the wavenumber: =. This is a linear dispersion relation, in which case the waves are said to be non-dispersive. [1] That is, the phase velocity and the group velocity are the same:
c is the speed of light in vacuum; h is the Planck constant. Whenever electromagnetic waves travel in a medium with matter, their wavelength is decreased. Wavelengths of electromagnetic radiation, whatever medium they are traveling through, are usually quoted in terms of the vacuum wavelength, although this is not always explicitly stated.
For the special case of an electromagnetic wave in a vacuum, in which the wave propagates at the speed of light, k is given by: = = where E is the energy of the wave, ħ is the reduced Planck constant, and c is the speed of light in a vacuum.
The velocity factor (VF), [1] also called wave propagation speed or velocity of propagation (VoP or ), [2] of a transmission medium is the ratio of the speed at which a wavefront (of an electromagnetic signal, a radio signal, a light pulse in an optical fibre or a change of the electrical voltage on a copper wire) passes through the medium, to the speed of light in vacuum.