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Group and Phase Velocity

  1. Dec 30, 2004 #1
    undefinedundefinedWhat are group velocity and phase velcity? What are it's physical implications? :rofl:
     
  2. jcsd
  3. Jan 1, 2005 #2
    Phase velocity is the speed in say degrees per sec of a single repeated waveform such as a sinewave which is travelling ( like a water wave ) past a point, 360 degrees being equivalent to one wavelength.
    If not a sinewave then wavelength here just refers to the distance between like points of a repetitive wave .
    However a waveform non sinusoidal can be viewed as made up of several or many other sine waves ( Fourier Analysis ) , if the medium (vaccuuo , air, glass etc , water )
    is non-dispersive , then all these waves travel at the same speed , and the wave shape is maintained -- but many materials ARE dispersive and differing wave lengths travel at different speed .
    This means that the wave shape will change with distance -- sometimes spreading out and sometimes being compressed.
    Group velocity refers to the speed of the peak intensity of that group of waves ( i.e.
    the points where they tend to reinforce ) , is therefore the speed of maximum energy.
    Group velocity is always less than or equal to the phase velocity.
    One slightly bizarre effect occurs in very thin ( hence transparent ) metal foils such as gold.
    Here the refractive index is the opposite of say glass , the implication being that light travels at > 'c' the velocity in vaccuuo. The explanation is given in terms of the 'group' or energy speed rather than individual sinewaves .
    Group velocity can also be taken to mean the information rate for the same reason.
    It has particular significance in the concepts of the photon as a 'pulse' of energy
    because again a pulse can be mathematically represented as a group of sinewaves which reinforce at only one point in space .
    Hope this helps Ray.
     
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