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The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as ... (where the wave speed is c 2 ...
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form:
Equations resembling those for the wave on a string can be written for the change in pressure ... c is the speed of the wave. To solve this differential equation, ...
Propagation of a wave packet demonstrating a phase velocity greater than the group velocity. This shows a wave with the group velocity and phase velocity going in different directions. The group velocity is positive, while the phase velocity is negative. [1] The phase velocity of a wave is the rate at which the wave propagates in any medium.
The wave equation describing a standing wave field in one dimension (position ) is p x x − 1 c 2 p t t = 0 , {\displaystyle p_{xx}-{\frac {1}{c^{2}}}p_{tt}=0,} where p {\displaystyle p} is the acoustic pressure (the local deviation from the ambient pressure) and c {\displaystyle c} the speed of sound , using subscript notation for the partial ...
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 .
The Dirac equation is a relativistic wave equation detailing electromagnetic interactions. Dirac waves accounted for the fine details of the hydrogen spectrum in a completely rigorous way. The wave equation also implied the existence of a new form of matter, antimatter, previously unsuspected and unobserved and which was experimentally confirmed.