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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".
The wavefronts of a traveling plane wave in three-dimensional space. In mathematics and physics , a traveling plane wave [ 1 ] is a special case of plane wave , namely a field whose evolution in time can be described as simple translation of its values at a constant wave speed c {\displaystyle c} , along a fixed direction of propagation n → ...
A plane wave is an important mathematical idealization where the disturbance is identical along any (infinite) plane normal to a specific direction of travel. Mathematically, the simplest wave is a sinusoidal plane wave in which at any point the field experiences simple harmonic motion at one frequency.
Because this is a plane wave, each blue vector, indicating the perpendicular displacement from a point on the axis out to the sine wave, represents the magnitude and direction of the electric field for an entire plane that is perpendicular to the axis. Represented in the second illustration is a circularly polarized, electromagnetic plane wave ...
Comparing our exact solution with the usual monochromatic electromagnetic plane wave as treated in special relativity (i.e., as a wave in flat spacetime, neglecting the gravitational effects of the energy of the electromagnetic field), one sees that the striking new feature in general relativity is the expansion and collapse cycles experienced ...
Mathematically, the simplest kind of transverse wave is a plane linearly polarized sinusoidal one. "Plane" here means that the direction of propagation is unchanging and the same over the whole medium; "linearly polarized" means that the direction of displacement too is unchanging and the same over the whole medium; and the magnitude of the displacement is a sinusoidal function only of time ...
In free space the wave impedance of plane waves is: = (where ε 0 is the permittivity constant in free space and μ 0 is the permeability constant in free space). Now, since = = (by definition of the metre),
In physics, the plane-wave expansion expresses a plane wave as a linear combination of spherical waves: = = (+) (^ ^), where . i is the imaginary unit,; k is a wave vector of length k,