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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.
In a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the phase speed is the speed of light, about 3 × 10 8 m/s.
In such a theory, its speed would depend on its frequency, and the invariant speed c of special relativity would then be the upper limit of the speed of light in vacuum. [32] No variation of the speed of light with frequency has been observed in rigorous testing, putting stringent limits on the mass of the photon. [ 59 ]
As a wave, light is characterized by a velocity (the speed of light), wavelength, and frequency. As particles, light is a stream of photons . Each has an energy related to the frequency of the wave given by Planck's relation E = hf , where E is the energy of the photon, h is the Planck constant , 6.626 × 10 −34 J·s, and f is the frequency ...
The primary properties of light are intensity, propagation direction, frequency or wavelength spectrum, and polarization. Its speed in vacuum , 299 792 458 m/s , is one of the fundamental constants of nature. [ 6 ]
The equation says the matter wave frequency in vacuum varies with wavenumber (= /) in the non-relativistic approximation. The variation has two parts: a constant part due to the de Broglie frequency of the rest mass ( ℏ ω 0 = m 0 c 2 {\displaystyle \hbar \omega _{0}=m_{0}c^{2}} ) and a quadratic part due to kinetic energy.
This startling coincidence in value led Maxwell to make the inference that light itself is a type of electromagnetic wave. Maxwell's equations predicted an infinite range of frequencies of electromagnetic waves, all traveling at the speed of light. This was the first indication of the existence of the entire electromagnetic spectrum.
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves).