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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.
For an incident wave traveling from one medium (where the wave speed is c 1) to another medium (where the wave speed is c 2), one part of the wave will transmit into the second medium, while another part reflects back into the other direction and stays in the first medium. The amplitude of the transmitted wave and the reflected wave can be ...
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 .
Wave speed is a wave property, which may refer to absolute value of: phase velocity , the velocity at which a wave phase propagates at a certain frequency group velocity , the propagation velocity for the envelope of wave groups and often of wave energy, different from the phase velocity for dispersive waves
In practice, g cannot have infinite periodicity because any real electromagnetic wave must always have a finite extent in time and space. As a result, and based on the theory of Fourier decomposition , a real wave must consist of the superposition of an infinite set of sinusoidal frequencies.
A common example of an NP problem not known to be in P is the Boolean satisfiability problem. Most mathematicians and computer scientists expect that P ≠ NP; however, it remains unproven. [16] The official statement of the problem was given by Stephen Cook. [17]
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