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| In [[physics]], '''front velocity''' is the speed at which the first rise of a pulse above zero moves forward.
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| In [[mathematics]], it is also used to describe the velocity of a possibly propagating front in the solution of [[hyperbolic partial differential equation]].
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| == Various velocities ==
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| Associated with propagation of a disturbance are several different velocities.<ref name="Milonni">{{cite book |title=Fast light, slow light and left-handed light |author=Peter W Milonni |url=http://books.google.com/books?id=kE8OUCvt7ecC&pg=PA26 |pages=26 ''ff'' |isbn=0-7503-0926-1 |year=2004 |publisher=CRC Press}}</ref> For definiteness, consider an [[amplitude modulation|amplitude modulated]] electromagnetic carrier wave. The [[phase velocity]] is the wave speed of the carrier. The [[group velocity]] is the wave speed of the modulation or [[envelope detector|envelope]]. Initially it was thought that the group velocity coincided with the speed at which ''information'' traveled. However, it turns out that this speed can exceed the speed of light in some circumstances, causing confusion by an apparent conflict with the [[theory of relativity]]. That observation led to consideration of what constitutes a ''signal''.
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| A signal involves new information or an element of 'surprise' that cannot be predicted from the wave motion at an earlier time.<ref name="Milonni" /> Thus, a possible form for a signal is:
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| :<math>f(t) = u(t) \sin \omega t \ , </math>
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| where ''u(t)'' is the [[Heaviside step function]]. Using such a form for a signal, it can be shown, subject to the (expected) condition that the refractive index of any medium tends to one as the frequency tends to infinity, that the wave discontinuity, called the ''front'', propagates at a speed less than or equal to the [[speed of light]] ''c'' in any medium.<ref name="Milonni" /> In fact, the earliest appearance of the front (the [[precursor (physics)|precursor]]) travels at the ''front velocity'' ''c'', ''no matter what the medium''.<ref name="Milonni" /><ref name="Stratton">{{cite book |title=Electromagnetic theory |author=Julius Adams Stratton |url=http://books.google.com/books?id=zFeWdS2luE4C&pg=PA337 |page=337 |isbn=0-470-13153-5 |publisher=Wiley/IEEE |year=2007 |edition=Classic reissue of 1941 }}</ref> However, the process always starts from zero amplitude and builds up.<ref name="Stratton" />
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| == References ==
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| <references/>
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| {{Velocities of Waves}}
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| [[Category:Wave mechanics]]
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| {{physics-stub}}
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Latest revision as of 11:01, 10 January 2015
Im addicted to my hobby Aircraft spotting.
I try to learn German in my spare time.
Feel free to visit my webpage Fifa 15 Coin Generator