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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 mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
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:
[note 1] The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law. Maxwell first used the equations to propose that light is an electromagnetic phenomenon.
The Andromeda Galaxy is approximately 2.5 million light-years away. 3 × 10 6 ly: The Triangulum Galaxy , at about 3 million light-years away, is the most distant object visible to the naked eye. 5.9 × 10 7 ly: The nearest large galaxy cluster, the Virgo Cluster, is about 59 million light-years away. 1.5 × 10 8 – 2.5 × 10 8 ly
Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave. [10] [11] Maxwell's equations were confirmed by Heinrich Hertz through experiments with radio waves. [12]
He obtained a wave equation with a speed in close agreement to experimental determinations of the speed of light. He commented, The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.
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.
Defining equation (physical chemistry) List of electromagnetism equations; List of equations in classical mechanics; List of equations in gravitation; List of equations in nuclear and particle physics; List of equations in quantum mechanics; List of equations in wave theory; List of relativistic equations