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Question from Beats (Waves)

Sanjeet asked:

"the displacement of a particle in periodic motion is given by "y=(cos2t-2cost+2sin^2t+1). What is the no. of beats that can be heard in 10 seconds?"

Propagation of Light, Group velocity and Phase velocity

Prasanna asks:

“how can light travel in the form of waves in space, which has no medium? if light doesn’t travel in the form of wave in the space then in equation. ‘phase velocity=c^2/group velocity ‘ phase velocity becomes zero and also c=0, which indicates velocity of light =0, but light actually travel in space . How can this be possible?”

Answer:

I feel that there is some sort of misunderstanding in your concept.

Why should phase velocity become zero?

Please remember that light is an electromagnetic wave, where the propagation is due to the mutually reinforcing time varying electric and magnetic field vectors varying in mutually perpendicular directions.

The phase velocity is a the speed at which a point of fixed phase (say the crust of the wave)  propagates, which is not always the speed at which the electromagnetic information travels.

Group velocity is the speed at which electromagnetic information travels.

Hope that the following links will help you sort out the issue.

  1. http://www.microwaves101.com/encyclopedia/phasevelocity.cfm
  2. http://en.wikipedia.org/wiki/Group_velocity
  3. http://en.wikipedia.org/wiki/Phase_velocity
  4. http://en.wikipedia.org/wiki/Speed_of_light
  5. http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SpeedOfLight/FTL.html

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