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| | | #REDIRECT [[Group velocity]] |
| #REDIRECT [[group velocity]] | |
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| {{TermHeader}}
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| <div class="termentry">
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| <div class="term">
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| == group velocity ==
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| #<div class="definition"><div class="short_definition">The [[velocity]] of the envelope of a group of waves of nearly equal frequencies.</div><br/> <div class="paragraph">From the [[dispersion relation]] ''k''(ω) the group velocity is defined as ''d''ω/''dk'', as distinguished from the [[phase velocity]] (or [[phase speed]]) ω/''k''. The origin of this term is made clearer by considering the superposition of two equal-amplitude plane [[harmonic]] waves with [[wavenumbers]] ''k'' ± Δ''k'' and frequencies ω ± Δω: <div class="display-formula"><blockquote>[[File:ams2001glos-Ge49.gif|link=|center|ams2001glos-Ge49]]</blockquote></div> Because <div class="inline-formula">[[File:ams2001glos-Gex05.gif|link=|ams2001glos-Gex05]]</div>, this composite [[wave]] may be looked upon as a high-frequency wave, with phase velocity ω/''k'', modulated by a wave of much lower [[frequency]] Δω. The envelope of the high- frequency wave is a low-frequency wave propagating with the group velocity Δω/Δ''k''. Note the similarity with [[beating]]. Indeed, a group of waves may be looked upon as a moving beat.</div><br/> </div>
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| #<div class="definition"><div class="short_definition">The [[velocity]] at which a group of waves, and the [[wave]] energy, travels.</div><br/> <div class="paragraph">In [[deep water]], on the basis of [[linear water wave theory]], it can be shown to be equal to one half the [[phase velocity]].</div><br/> </div>
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| {{TermIndex}}
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| [[Category:Terms_G]]
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