What is the relationship between group and phase velocity?

[saiarun]

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

 

[rayjohn01]

Phase velocity is the speed in say degrees per sec of a single repeated waveform such as a sinewave which is traveling ( 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.