## Group and Phase Velocity

undefinedundefinedWhat are group velocity and phase velcity? What are it's physical implications?
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 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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