Phase velocity derivation

1. What is phase velocity and its formula?
2. Is phase velocity particle velocity?
3. What is the value of phase velocity?

What is phase velocity and its formula?

A plane wave traveling in the + z direction can be written as sin k z − ω t . The wave moves at a speed that keeps the argument of the sine function a constant. For convenience, this constant is chosen to be zero and the argument becomes k z − ω t = 0 . Rearranging this equation gives z / t = ω / k .

Is phase velocity particle velocity?

The velocity v of the electron in the free electron gas model is the velocity with which the phase of the wave moves, it is called phase velocity v_P. As long as a single plane wave symbolizes all that is to a particle, the phase velocity is automatically also the particle velocity v.

What is the value of phase velocity?

In vacuum, the phase velocity is c = 299 792 458 m/s, independent of the optical frequency, and equals the group velocity. In a medium, the phase velocity is typically smaller by a factor n, called the refractive index, which is frequency-dependent (→ chromatic dispersion).