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Wave equation. 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.
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. [9] [10] Maxwell's equations were confirmed by Heinrich Hertz through experiments with radio waves. [11]
This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and time period T as. Equivalently, in terms of the wave's angular ...
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.
Electromagnetic wave equation. 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 ...
c is the speed of the wave; and; ω is the angular frequency of the wave. The quantity x/c is the time that the wave takes to travel the distance x. The ordinary frequency (f) of the wave is given by =. The wavelength can be calculated as the relation between a wave's speed and ordinary frequency.
The first general equation of motion developed was Newton's second law of motion. In its most general form it states the rate of change of momentum p = p(t) = mv(t) of an object equals the force F = F(x(t), v(t), t) acting on it, [13]: 1112. The force in the equation is not the force the object exerts.
Wave-particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances. [1]: 59 It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects. [2]: III:1-1 During the 19th and early 20th ...
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