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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.
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".
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 .
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.
A superposition of 1D plane waves (blue) each traveling at a different phase velocity (traced by blue dots) results in a Gaussian wave packet (red) that propagates at the group velocity (traced by the red line). The group velocity of a collection of waves is defined as =.
Tracing the y component of a circle while going around the circle results in a sine wave (red). Tracing the x component results in a cosine wave (blue). Both waves are sinusoids of the same frequency but different phases. A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine ...
A man who raped a vulnerable woman after posing as a good samaritan and luring her to his Aberdeen flat has been jailed for five years. Diego Valdivieso, 30, offered the young woman a bed at his ...
The term alternating current applies to a voltage vs. time function that is sinusoidal with a frequency f. When it is applied to a typical (linear time-invariant) circuit or device, it causes a current that is also sinusoidal. In general there is a constant phase difference φ between any two sinusoids. The input sinusoidal voltage is usually ...