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# Topic: Group velocity

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 Group velocity - Wikipedia, the free encyclopedia The group velocity of a wave is the velocity with which the variations in the shape of the wave's amplitude (known as the modulation or envelope of the wave) propagate through space. The group velocity is often thought of as the velocity at which energy or information is conveyed along a wave. This "group velocity dispersion" is an important effect in the propagation of signals through optical fibers and in the design of short pulse lasers. en.wikipedia.org /wiki/Group_velocity   (496 words)

 Phase velocity - Wikipedia, the free encyclopedia The phase velocity of a wave is the rate at which the phase of the wave propagates in space. Note that the phase velocity is not necessarily the same as the group velocity of the wave, which is the rate that changes in amplitude (known as the envelope of the wave) will propagate. The phase velocity of electromagnetic radiation may under certain circumstances exceed the speed of light in a vacuum, but this does not indicate any superluminal information or energy transfer. en.wikipedia.org /wiki/Phase_velocity   (305 words)

 Group Velocity Demonstration   (Site not responding. Last check: 2007-11-07) The quantity we commonly refer to as the "speed-of-light" is its phase velocity: the speed at which the wavefronts of a pure frequency tone travel. The group velocity is the speed at which pulses (or "wave packets"), which are made up of a range of spectral components, travel. The group velocity and phase velocity are the same in a vacuum, but in any other medium this is not, in general, the case. www2.ee.mu.oz.au /staff/summer/applets/group_velocity.html   (524 words)

 Phase and Group Velocity   (Site not responding. Last check: 2007-11-07) PURPOSE: To demonstrate the relationship between the phase velocity and the group velocity of a wavepacket. The group velocity is seen to move rapidly across the picture, as shown in the photo at right. The movement of the phase velocity (motion of each transparency) is much slower than the fast moving group velocity. www.physics.brown.edu /physics/demopages/Demo/waves/demo/3b3320.htm   (272 words)

 Phase versus Group Velocity   (Site not responding. Last check: 2007-11-07) This animation shows the difference between phase velocity and group velocity in a traveling wave packet. The phase velocity is the speed of the individual wave crests, whereas the group velocity is the speed of the wave packet as a whole (the envelope). In this case, the phase velocity is greater than the group velocity. www.geneseo.edu /~freeman/animations/phase_versus_group_velocity.htm   (55 words)

 Global models of Surface Wave Group Velocity   (Site not responding. Last check: 2007-11-07) Measurements of group velocity are derived from phase velocity dispersion curves and are modeled with global laterally-varying isotropic structure. The group velocity maps from this study are compared for the area of Eurasia with the maps of Ritzwoller and Levshin [1998]. The global maps are useful for prediction of group arrival times, for revealing tectonic structures, and as a basis for regional group velocity studies. www.seismology.harvard.edu /projects/surfwave/LE00-Pageoph/summary.html   (299 words)

 Encyclopedia of Laser Physics and Technology - group velocity, light, envelope The group velocity of light in a medium is defined as the inverse of the derivative of the wavenumber with respect to angular frequency: The group velocity is the velocity with which the envelope of a pulse propagates in a medium, assuming a long pulse with narrow bandwidth (so that higher-order chromatic dispersion is not relevant) and the absence of nonlinear effects (i.e., low enough optical intensities). Due to dispersion, the group velocity in a medium is in general different from the phase velocity (typically smaller than the latter), and it is frequency-dependent; this effect is called group velocity dispersion. www.rp-photonics.com /group_velocity.html   (385 words)

 BBC News | SCI/TECH | Beam smashes light barrier The group velocity of a light pulse depends upon the mixture of frequencies within the pulse and the medium through which it travels. The important thing, however, is that whilst the group velocity can be manipulated to be faster than the speed of light, it is not possible to use this effect to send information faster than the speed of light. Because of the fast group velocity, the leading edge of the pulse appears to leave the caesium-filled chamber 62 billionths of a second before it arrives. news.bbc.co.uk /1/hi/sci/tech/841690.stm   (523 words)

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 Phase, Group, and Signal Velocity The velocity of a wave can be defined in many different ways, partly because there many different kinds of waves, and partly because we can focus on different aspects or components of any given wave. In a medium whose refractive index is constant, independent of frequency (such as the vacuum), we have dn/dk = 0 and therefore the group velocity equals the phase velocity. It follows that the group velocity of light in such media (called dispersive) is less than the phase velocity. www.mathpages.com /home/kmath210/kmath210.htm   (1990 words)

 GroupVelocity   (Site not responding. Last check: 2007-11-07) The phase velocity is fixed at 1.0 (arbitrary units). As long as the group velocity is set equal to one, the wavepackets move at the same speed as the individual waves. In this case the the phase velocity is twice the group velocity, so as the wave propagates the individual waves disappear at the trailing edge of the packet. physics.berea.edu /~king/Teaching/ModPhys/QM/Wave/GroupVelocity.html   (377 words)

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 Encyclopedia of Laser Physics and Technology - group velocity dispersion Definition: the frequency dependence of the group velocity in a medium, or (quantitatively) the corresponding derivative with respect to angular frequency Group velocity dispersion is the frequency (or wavelength) dependence of the group velocity of light in a medium. Group velocity dispersion is responsible for dispersive broadening of pulses and for the group velocity mismatch of different waves in parametric nonlinear interactions. www.rp-photonics.com /group_velocity_dispersion.html   (183 words)

 PIRA 3B33.00 PHASE AND GROUP VELOCITY   (Site not responding. Last check: 2007-11-07) Measuring group velocity using two sine waves and an oscilloscope. This group and phase velocity device was made from an apple peeler. phase and group velocity on the OH A sheet with fl bands is pulled across an overhead projector covered except for slits parallel, perpendicular, and at 45 degrees to the motion. www.wesleyan.edu /physics/demos/pirabib/3oandw/3B33.html   (242 words)

 Group Velocity   (Site not responding. Last check: 2007-11-07) Stationary group where the group velocity is zero. Moving group where the phase velocity is zero. Moving group and phase where both velocities are nonzero. krypton.mnsu.edu /~7364eb/Math113/groupvelocity.html   (158 words)

 Group Velocity Transparencies   (Site not responding. Last check: 2007-11-07) Wave groups move rapidly across the picture while the wave velocity is much smaller. Wave velocity, seen as the motion of the transparency, can be seen by a marks on the transparencies. Superimpose two combs on the overhead projector to show phase and group velocity. demoroom.physics.ncsu.edu /html/demos/495.html   (141 words)

 Definition: group velocity   (Site not responding. Last check: 2007-11-07) The velocity of propagation of an envelope produced when an electromagnetic wave is modulated by, or mixed with, other waves of different frequencies. Note: The group velocity is the velocity of information propagation and, loosely, of energy propagation. In optical fiber transmission, for a particular mode, the reciprocal of the rate of change of the phase constant with respect to angular frequency. www.atis.org /tg2k/_group_velocity.html   (129 words)

 Group Velocity Whatever this relationship turns out to be in a particular case, it is called the dispersion relation for the type of wave in question. As an example of a group velocity calculation, suppose we want to find the velocity of deep ocean wave packets for a central wavelength of It is easy to show that dispersive waves have unequal phase and group velocities, while these velocities are equal for non-dispersive waves. www.physics.nmt.edu /~raymond/classes/ph13xbook/node16.html   (211 words)

 Phase, group velocity and energy I know the definitions of phase and group velocity from here and what they look like from here. Essentially, the energy of a wave is dependant on the amplitude, which is why the envelope of the wave is associated with the energy of the wave rather than the rapid oscillatory component. The group velocity thus features in equations for power flow and energy and so forth because the group velocity describes the propagation of the envelope. www.physicsforums.com /showthread.php?t=96835   (249 words)

 PHASE AND GROUP VELOCITY AIM: To demonstrate the difference between phase and group velocity. DESCRIPTION: Two signal generators are connected to separate channel inputs on the four channel C.R.O. The third channel contains the sum of the two signals via the isolating resistors. If the two frequencies of the oscillators are approximately equal the resulting waveforms adequately demonstrate the phase and group velocity of the packet. www.ph.unimelb.edu.au /staffresources/lecdem/wa2.htm   (62 words)

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 Harvard Seismology: Group velocity models We have inverted for models of surface wave group velocity at periods between 35 s and 175 s. The method and results are described in Global models of surface wave group velocity. We inverted separately for Love and Rayleigh waves at each period for a model parameterized with spherical harmonics up to degree 40. www.seismology.harvard.edu /projects/surfwave/LE00-Pageoph   (179 words)

 [ Velocity Resource Group ]   (Site not responding. Last check: 2007-11-07) Velocity Resource Group services are marketed to any entity seeking to access active job candidate resumes in a timely and cost effective mannerâ¦â¦ Whether you are hiring Entry Level or Senior Executives, Velocity Resource Group identifies targeted candidates for your organizational needsâ¦ Velocity Resource Group services are effective in all industries and areas of functional specializationâ¦â¦ www.velocityresourcegroup.com /005.html   (111 words)

 Group velocity in noncommutative spacetime   (Site not responding. Last check: 2007-11-07) We focus here on κ-Minkowski spacetime, a much-studied example of Lie-algebra noncommutative spacetime, but our analysis appears to be applicable to a more general class of noncommutative spacetimes. A technical controversy which has significant implications for experimental testability is the one concerning the κ-Minkowski relation between group velocity and momentum. While in these previous studies the relation between group velocity and momentum was introduced through ad hoc formulae, we rely on a direct analysis of wave propagation in κ-Minkowski. stacks.iop.org /1475-7516/2003/i=09/a=006   (344 words)

 Phase vs. Group Velocity   (Site not responding. Last check: 2007-11-07) (26) we find that the phase velocity is higher for smaller It has been passing by forever and will continue to do so forever; it is the same amplitude everywhere; and so on. The general definition of the group velocity (the speed of transmission of information and/or energy in a wave packet) is musr.physics.ubc.ca /~htb/phys/Waves/node12.html   (318 words)

 Group Velocity   (Site not responding. Last check: 2007-11-07) Overlay the transparencies on the overhead projector and move one with respect to the other to demonstrate the difference between the phase velocity (that of the transparency) and the group velocity (that of the moire pattern). This can also be shown with a pair of combs. A java applet showing group and phase velocity: www.oberlin.edu /physics/catalog/demonstrations/waves/groupvel.html   (81 words)

 Phase and Group Velocities of Wave Packets The following movies show wave packets with various combinations of phase and group velocity. Each waveform is the sum of five sinusoids with the general format I take full responsibility for the information presented and will appreciate being informed of errors or inaccuracies. www.csupomona.edu /~ajm/materials/animations/packets.html   (194 words)

 Letter to the Editor   (Site not responding. Last check: 2007-11-07) The Bruggeman formalism is implemented to estimate the refractive index of an isotropic, dielectric, homogenized composite medium (HCM). Invoking the well-known Hashin–Shtrikman bounds, we demonstrate that the group velocity in certain HCMs can exceed the group velocities in their component materials. In particular, reselling and systematic downloading of files is prohibited. stacks.iop.org /0305-4470/37/L19   (228 words)

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