To understand the difference between phase and group velocity of waves, consider the following analogy. A group of people, say city marathon runners, start from the starting at the same time. Initially it would appear that all of them are running at the same speed. As time passes, group spreads out (disperses) simply because each runner in the group is running with different speed. If you think of phase velocity to be like the speed of an individual runner, then the group velocity is the speed of the entire group as a whole. Obviously and most often, individual runners can run faster than the group as a whole. To stretch this analogy, we note that the phase velocity vp of waves are typically larger than the group velocity vg of waves. However, this really depends on the properties of the medium. The media in which vg = vp is called the non-dispersive medium. But the media in which vg < vp is called normal dispersion. The media in which vg > vp is called anomolous dispersive media.
Believe me Sir, I was totally scared of this subject till now. Your videos have helped me understand this subject in a thorough manner. Thank you so much. :)
Phase velocity is always greater then velocity of light. Phase velocity is associated with total path length of light. Here total path length is always more then the distance travel by light .
@@dewadattaa268 I think phase velocity is just a theoretical concept which can explain certain phenomenons. After watching this video, my understanding is that it is the velocity of constant phase points which is measured along the directions of propagation of the wave which is clearly in z-axis.
@@gokulnathsj219 I have been puzzled by a statement a colleague made. I found the following, but I am not sure it makes sense to me. van.physics.illinois.edu/qa/listing.php?id=16704&t=faster-than-speed-of-light
Hi I'm really struggling with this argument; so from what you say PHASE velocity is just a projection of the Group one, so an algebric abstraction, right? Now my question is what happen if the wave's propagation direction is z itself? Group and phase velocity are the same? So it would mean that there will not be a dispersive material anymore? But in that case it means that having different phase and group velocity is just a matter of field orientation, no relatated to the material anymore... PLEASE HELP:).
Group and phase velocity is not dependent on materials. It is dependent on modes of operation and operating frequency. So yes ... It is based on field orientation. Field dispersion is different problem and it depends on loss tangent of materials. I hope I would have replied to your question.
Thanks for your reply but I don't think of having fully understood it. Let's say I have a dispersive planar waveguide so that omega(k) is not a line, if I send in it packet of frequency and each of them is for example TE mode, and propagates in the same direction z, will I have the same phase and gruop velocity ?
Phase velocity is always greater then group velocity. And remember phase velocity is even greater then velocity of light. So think about physical path travel and actual path travel. I think now you will find your answer. Here it's bit difficult to explain by writing.
