Search results
Results from the WOW.Com Content Network
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".
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 .
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 ...
Therefore, u and v, or Re(A) and Im(A), are sinusoidal functions of space and time. These exact solutions for the periodic travelling wave families enable a great deal of further analytical study. Exact conditions for the stability of the periodic travelling waves can be found, [ 1 ] [ 2 ] and the condition for absolute stability can be reduced ...
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.
Because of its many applications in information theory, physics and engineering there exist alternative names for specific linear response functions such as susceptibility, impulse response or impedance; see also transfer function. The concept of a Green's function or fundamental solution of an ordinary differential equation is closely related.