The phase velocity can be thought of as the speed of a pure monochromatic wave or the speed of a single frequency. Specifically, it is the speed of the peaks and troughs that make up the wave.
The group velocity can be thought of as the speed of the propagating temporal interference pattern produced by multiple spectral components traveling at different speeds in a material. Since a pulse is made up of many spectral components, the group velocity is usually associated with the speed of pulse propagation.
rayjohn01 said:
These concepts are based on the idea of a traveling wave -- i.e. think of a water wave which is a single traveling sinusoid.
If you assemble a group of such waves( of different frequency ) they reinforce and cancel each other at regular intervals .
True. That is what I mean above by temporal interference.
If they are all traveling at the same rate the peak of the group travels at a different rate than the individuals -- this is group velocity.
No, this is not true. If the different components of the wave are all traveling at the same speed, there is no dispersion (by definition). In such situations, the peak will travel exactly at the same speed of the components since the interference pattern will not change. Hence, in the situation you describe, the phase velocity will equal the group velocity. The group velocity will only become different than the phase velocity when you have dispersion.
Group velocity is the speed with which the average information about the whole group travels and is always less than the wave velocity -- this is exemplified in metals which have a -ve refractive index indicating that the wave velocity is > than light in vaccuo , but the group velocity is less than light .
Not true. Do not confuse the information velocity and the group velocity. The group velocity is often equal to the information velocity, but that is not always true. Also, the group velocity is
not always less than the phase velocity. The group velocity can be much, much less than
c (~10 m/s), equal to
c, greater than
c, or even negative.
Negative group velocities are the case where the anomalous dispersion (higher frequency light travels faster than lower frequency light) is so large that peak of the pulse exits the material before it enters. While this seems to violate causality, a careful examination reveals that the pulse is actually reshaped so that the leading edge of the pulse becomes the new peak and the old peak becomes absorbed (and forms the trailing edge of the new pulse). A good paper that deals with this issue of negative group velocities and information velocity is Stenner et al., Nature 425, 695 (2003).
This is simply illustrated by sine waves there is no paradox here.
True, but there seems to be a lot of confusion. Stunner, do a google search on "group velocity." There are many helpful sites out there on the subject.
