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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 same sinusoidal plane wave above can also be expressed in terms of sine instead of cosine using the elementary identity = (+ /) (,) = ((^) + ′) where ′ = + /.Thus the value and meaning of the phase shift depends on whether the wave is defined in terms of sine or co-sine.
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.
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 → ...
In electromagnetic theory, the phase constant, also called phase change constant, parameter or coefficient is the imaginary component of the propagation constant for a plane wave. It represents the change in phase per unit length along the path traveled by the wave at any instant and is equal to the real part of the angular wavenumber of the
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).
The plane wave spectrum representation of a general electromagnetic field (e.g., a spherical wave) in the equation is the basic foundation of Fourier optics (this point cannot be emphasized strongly enough), because at z = 0, the equation simply becomes a Fourier transform (FT) relationship between the field and its plane wave contents (hence ...
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 ...