Phase Velocity vs. Group Velocity

Main Difference

The main difference between phase velocity and group velocity is that phase velocity is always greater than the group velocity in a normal medium, whereas group velocity is smaller than the phase velocity in a normal medium.

Difference Between Phase Velocity and Group Velocity

Comparison Chart

Phase Velocity vs. Group Velocity

The phase velocity is the characteristic of the individual wave, while group velocity is the characteristic of the group of waves. In an ordinary medium, the phase velocity is always considered greater than the group velocity, while in an anomalous medium, the group velocity is considered greater than the phase velocity.

The carrier waves travel with the phase velocity in a wave packet; on the contrary, the envelope travels with the group velocity in a wave packet. The formula of the phase velocity is v_p = ω/k = λf; on the flip side, the formula of the group velocity is v_g = dω/dk = v_p + k (dv_p/dk). The phase velocity in mathematical form is the ratio of angular frequency to wave vector, while the group velocity in mathematical form is the ratio of change in angular frequency to change in wave vector.

The phase is usually defined for both the single waves and superimposed waves; on the other hand, the group velocity is only defined for the superimposed waves. The phase velocity is considered as the velocity of the wave with higher frequency; on the contrary, the group velocity is generally the velocity of the wave with lower frequency.

In phase velocity, when we deal with individual waves, the phase velocity plays an important role; on the other hand, when a particle is represented by waves, then the concept of group velocity plays an important role. The phase velocity for non-relativistic, v_p = v/2 and for relativistic particle, v_p = c² /v; on the other hand, the group velocity for non-relativistic particles and relativistic particles is, v_g = v.

What is Phase Velocity?

The velocity of a wave in which any given phase of the wave travels is known as the phase velocity of a wave. For instance, a wave having point A travels with phase velocity. The phase velocity is given by v_p=ωk.

The carrier waves travel with the phase velocity in the medium of the wave packet. But many times, the phase velocity isn’t important when we are talking about a particle or a wave packet.

The association between the phase velocity and the group velocity always depends on the properties of the materials of the medium. In non-dispersive mediums, phase velocity equivalents to the group velocity. In normal dispersion mediums, the phase velocity is greater than the group velocity. In anomalous mediums, the phase velocity is smaller than the group velocity.

The phase velocity of many waves does not usually depend on the wavelength in non-dispersive mediums. So, the phase velocity always equals the group velocity in a non-dispersive medium. Such as when sound waves propagate through the air because air acts as a non-dispersive medium so that the phase velocity will be equal to the group velocity.

What is Group Velocity?

The velocity with which a group of waves amplitudes travels through space is the group velocity of a wave. It can be understanding with the help of a simple example of a race in which any given instant, the velocity of a specific runner is dissimilar with the others, which means every runner has different velocities. But every one of them is running in a group. So, the velocity in which runners are moving is known as the group velocity.

The concept of group velocity comes to the idea of wave packets or pulses in quantum physics. When many waves with different velocities, numbers, and amplitudes are combined, then the wave packet can be obtained. Hence, the position of a specific particle can be identified in a specific region by using wave packets, which represents a particle.

The monochromatic waves cannot transmit information via space. So, to transmit this information, the superposition of many waves, which generally gives wave packets is needed.

The group velocity is defined with the help of an equation v_g = dω/dk in which ω is the wave’s angular frequency, and k is the angular wavenumber. If ω is sometimes directly proportional to k, then the group velocity will be equal to the phase velocity, or else the wave’s envelope will become partisan when it transmits.

Conclusion

The above discussion concludes that the phase velocity is considered as the characteristic for the individual waves; on the other hand, the group velocity is considered as the characteristic for the group of velocities.