Questio was: can i have an expression between particle velocity and wave velocity

Answer by Adapa Bharath: Dear Abhinav,

The concept of particle velocity and wave velocities come in case of a wave packet or group wave....

The particle velocity is nothing but the group velocity v_g=dω/dk. And wave velocity is v=ω/k

which implies ω = v*k substituting this we get v_g=( dv/dk )* k + v

Now my question is: Shouldn't be the group velocity always less than the wave velocity, as the Einstein says about the velocity of light, which cannot be overpassed? The above formula states the opposite. Or may be I am wrong, but where?

Dear Student,

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.

Best Of luck

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You gave me no answer to my specific questions; you just stated definitions of phase and group velocity, which I did not ask, because I already know them.

What I asked was:

v_g=( dv/dk )* k + v ; this is the formula you wrote

 Shouldn't be the group velocity always less than the wave velocity, as the Einstein says about the velocity of light, which cannot be overpassed? The above formula states the opposite. Can you explain this to me, please?

Dear friend,

Group velocity is similar to phase velocity or wave velocity rather than particle velocity as you mentioned. thats why you are confused with the results you are discussing.