How do you find group velocity from phase velocity?

In a given medium, the frequency is some function ω(k) of the wave number, so in general, the phase velocity vp= ω/k and the group velocity vg = dω/dk depend on the frequency and on the medium. The ratio between the speed of light c and the phase velocity vp is known as the refractive index, n = c/vp = ck/ω.

At what condition VP is equal to VG?

Generally, ω(k) is called the dispersion relation and indicates the dispersion properties of a medium. As this formula predicts, if the phase velocity does not depend on the wavelength of the propogating wave, then vg = vp.

What is difference between group velocity and phase velocity?

Phase velocity is defined for both, the single waves and superimposed waves. The group velocity is defined only to the superimposed waves. The group velocity is the velocity of the wave with lower frequency, but the phase velocity is the velocity of the wave with higher frequency.

What is meant by phase velocity and group velocity?

The phase velocity is given in terms of the wavelength ` lambda ` and period T as `v_(rho) = (lambda)/(T) = (omega)/(K)` Group velocity : The group velocity of a wave is the velocity of a move group (like a beat) `v_(g) = (d omega)/( dk)` Where, ` omega ` = angular frequency.

What is the product of phase velocity and group velocity?

The product between the phase velocity and the group velocity of any particle (massive or massless) equals the square of the speed of light in vacuum. The group velocity of any particle (massive or massless) is equal to the derivative of its total relativistic energy with respect to its relativistic momentum.

Is group velocity greater than phase velocity?

For most substances, therefore, the group velocity is smaller than the phase velocity. In such cases, it is mathematically possible that the group velocity may be larger than the phase velocity.

What do you mean by phase velocity and group velocity find a relation between them?

Mathematical Relation Between Group Velocity and Phase Velocity. Following is the derivation of the relation of the Group Velocity and the Phase Velocity. To find out the amplitude of wave packet let us assume, ω as the angular velocity given by ω = 2πf. k as the angular wavenumber given by – k = 2π / λ

What is the relation between group velocity and phase velocity?

The velocity with which the phase of a wave travels is called phase velocity. The relation between group velocity and phase velocity are proportionate. V g is the group velocity.

What is the phase velocity of a wave?

Considering the fact that a wave consists of two significant parts crest and trough, its phase velocity is also dependent on the same. Students should have prior knowledge of it to understand what phase velocity is. It is the velocity at which a specific component of a wave, say crest, propagates in space.

What is the group velocity of a non-relativistic free particle?

Thus for a non-relativistic free particle the group velocity (vg) is twice of the phase velocity (u). 1. In a normal medium, the phase velocity is greater than the group velocity. In an anomalous medium, the group velocity is greater than the phase velocity.