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In linear uniform media, a general solution to the wave equation can be expressed as a superposition of sinusoidal plane waves. This approach is known as the angular spectrum method. The form of the planewave solution is actually a general consequence of translational symmetry.
Sinusoidal plane-wave solutions are particular solutions to the wave equation. The general solution of the electromagnetic wave equation in homogeneous, linear, time-independent media can be written as a linear superposition of plane-waves of different frequencies and polarizations .
The term is also used, even more specifically, to mean a "monochromatic" or sinusoidal plane wave: a travelling plane wave whose profile () is a sinusoidal function. That is, (,) = (() +) The parameter , which may be a scalar or a vector, is called the amplitude of the wave; the scalar coefficient is its "spatial frequency"; and the scalar is its "phase shift".
Still, it can be analyzed as a linear combination of simple solutions that are sinusoidal plane waves with various directions of propagation and wavelengths but all with the same propagation speed c. This analysis is possible because the wave equation is linear and homogeneous, so that any multiple of a solution is also a solution, and the sum ...
A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine function. In mechanics , as a linear motion over time, this is simple harmonic motion ; as rotation , it corresponds to uniform circular motion .
A sinusoidal plane wave is one special solution of these equations. Maxwell's equations explain how these waves can physically propagate through space. The changing magnetic field creates a changing electric field through Faraday's law.
Of these, the most important examples are the electromagnetic plane waves, in which the radiation has planar wavefronts moving in a specific direction at the speed of light. Of these, the most basic is the monochromatic plane waves, in which only one frequency component is present. This is precisely the phenomenon that this solution model, but ...
Download as PDF; Printable version; In other projects ... and applied mathematics), physics, engineering, economics ... Plane curves of degree 2 are known as conics ...