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Wave vector - Wikipedia, the free encyclopedia
The wave vector has magnitude indicating wavenumber (reciprocal of wavelength) ... Taking the Lorentz transform of the wave vector is one way to derive the ...
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wave vector: Definition from Answers.com
wave vector ( ?w?v ?vekt?r ) ( physics ) A vector whose direction is the direction of phase propagation of a wave at each point in space, and whose
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Waves/Vectors - Wikibooks, collection of open-content textbooks
Waves/Vectors. From Wikibooks, the open-content textbooks collection < Waves ... Before we can proceed further we need to explore the idea of a vector. ...
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Wave Vector -- from Eric Weisstein's World of Physics
Wave Vector. The wave vector k has magnitude equal to the wavenumber k (1) (2) (3) and orientation in the direction of wave propagation. ...
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Royalty Free Stock Vector Art & Illustrations: wave | iStockphoto.com
Royalty Free Stock Vector Art & Illustrations, wave, copyright penfold, iStockphoto LP ... HOW > Style and Design > Illustrations > Vector Miscellaneous ...
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Sound Waves
Vector Calculus. Equations of Motion. Velocity Potential. Spherical Waves. New Solutions From Old ... so all the important quantities of the wave can be ...
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DOE Document - ASYMPTOTIC WAVE VECTOR AND NONRELATIVISTIC PERTURBATION ...
The Energy Citations Database (ECD) provides access to historical and current research ... A wave vector initially represented in terms of a set of unperturbed ...
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Special Relativity/Waves - Wikibooks, collection of open-content textbooks
The large arrow is the associated wave four-vector, which has slope ? / ck. ... Applying this to the wave four-vector, we infer that ...
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Molecular Expressions Microscopy Primer: Polarized Light Waveforms ...
... phase shift between the waves) when the electric field vectors are added ... by calculating the sum of the electric vector components from each wave. ...
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A wave vector is a vector (spatial) that specifies the wavenumber and direction of propagation for a wave. The magnitude of the wave vector indicates the wavenumber. The orientation of the wave vector indicates the direction of wave propagation.

For example consider a plane wave. A common representation of the oscillation at time (t) and a single point in space (z) along the direction of propagation is: \psi \left(t , z\right) = A \cos \left(\varphi + k z + \omega t\right) where A is the amplitude, φ is the starting phase of the wave, k is the angular wavenumber, and ω is the angular frequency. We can easily extend the formula by substituting the dot product of the wave vector k and the position vector r for the scalar product of the wavenumber k and the variable z as follows: \psi \left(t , {\mathbf r} \right) = A \cos \left(\varphi + {\mathbf k} \cdot {\mathbf r} + \omega t\right).

In special relativity A wave packet of nearly monochromatic light can be characterized by the wave vector :k^\mu = \left(\frac{\omega}{c}, \vec{k} \right) \, which, when written out explicitly in its covariant and contravariant forms is :k^\mu = \left(\frac{\omega}{c}, k^1, k^2, k^3 \right)\, and :k_\mu = \left(\frac{\omega}{c}, -k_1, -k_2, -k_3 \right) . \,

The magnitude of this wave vector is then :k^2 = k^\mu k_\mu = k^0 k_0 - k^1 k_1 - k^2 k_2 - k^3 k_3 \, ::::=\frac{\omega^2}{c^2} - \vec{k}^2 = 0. \,

That last step where it equals zero, is a result of the fact that, for light, :k = \frac{\omega}{c}. \,

Lorentz transform Taking the Lorentz transform of the wave vector is one way to derive the Relativistic Doppler effect. The Lorentz matrix is defined as :\Lambda = \begin{pmatrix} \gamma&-\beta \gamma&0&0 \\-\beta \gamma&\gamma&0&0 \\0&0&1&0 \\0&0&0&1\end{pmatrix}.

In the situation where light is being emitted by a fast moving source and one would like to know the frequency of light detected in an earth (lab) frame, we would apply the lorentz transform as follows. Note that the source is in a frame Ss and earth is in the observing frame, Sobs.Applying the lorentz transformation to the wave vector :k^{\mu}_s = \Lambda^\mu_\nu k^\nu_{\mathrm{obs--> \,

and choosing just to look at the \mu = 0 component results in :k^{0}_s = \Lambda^0_0 k^0_{\mathrm{obs--> + \Lambda^0_1 k^1_{\mathrm{obs--> + \Lambda^0_2 k^2_{\mathrm{obs--> + \Lambda^0_3 k^3_{\mathrm{obs--> \, :{| |\frac{\omega_s}{c} \,|= \gamma \frac{\omega_{\mathrm{obs-->}{c} - \beta \gamma k^1_{\mathrm{obs--> \,|-||\quad = \gamma \frac{\omega_{\mathrm{obs-->}{c} - \beta \gamma \frac{\omega_{\mathrm{obs-->}{c} \cos \theta. \,|}So :{|cellpadding="2" style="border:2px solid #ccccff" |\frac{\omega_{\mathrm{obs-->}{\omega_s} = \frac{1}{\gamma (1 - \beta \cos \theta)} \,|}

Source moving away As an example, to apply this to a situation where the source is moving directly away from the observer (\theta=\pi), this becomes: :\frac{\omega_{\mathrm{obs-->}{\omega_s} = \frac{1}{\gamma (1 + \beta)} = \frac{\sqrt{1-\beta^2-->{1+\beta} = \frac{\sqrt{(1+\beta)(1-\beta)-->{1+\beta} = \frac{\sqrt{1-\beta-->{\sqrt{1+\beta--> \,

Source moving towards To apply this to a situation where the source is moving straight towards the observer (\theta=0), this becomes: :\frac{\omega_{\mathrm{obs-->}{\omega_s} = \frac{\sqrt{1+\beta-->{\sqrt{1-\beta--> \,

References

Wave vector - Wikipedia, the free encyclopedia
A wave vector is a vector representation of a wave. The wave vector has magnitude indicating wavenumber (reciprocal of wavelength), and the direction of the vector indicates the ...

University of Sussex Research Online - Instantaneous local wave ...
Cluster is the first space mission for which direct determination of the full 3-dimensional local wave vector is possible, as described here.

Wave vector - What does WV stand for? Acronyms and abbreviations by ...
All content on this website, including dictionary, thesaurus, literature, geography, and other reference data is for informational purposes only.

Wave Vector -- from Eric Weisstein's World of Physics
The wave vector k has magnitude equal to the wavenumber k k = \left\vert{\mathbf{k}}\right\vert = {2\pi\over \lambda} = \sqrt{k_x^2+k_y^2+k_z^2} and orientation in the direction ...

Method for the generation of arbitrary complex vector*wave fronts
Method for the generation of arbitrary complex vector wave fronts Method for the generation of arbitrary complex vector*wave fronts

The Wave-Vector Dependence of Quantum Evaporation from Superfluid 4He
C.D.H. Williams 2/6 WILLIAMS heater bolometer φ b θ h collimation collimation liquid vacuum Fig. 1. Schematic diagram of a quantum evaporation experiment.

wave vector: Definition from Answers.com
wave vector ( ′wāv ′vektər ) ( physics ) A vector whose direction is the direction of phase propagation of a wave at each point in space, and whose

PROCESSING AND INTERPRETING VECTOR WAVE-FIELD DATA
canadian journal of exploration geophysics vol. 29, no. (june 1993), p. 117-124 processing and interpreting vector wave-field data p hilip wild', colin m ac b eth ', stuart crampin ...

wave vector - Wiktionary
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WV
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