What is the difference between group velocity and phase velocity?

What is the difference between group velocity and phase velocity?

Waves can be in the group and such groups are called wave packets, so the velocity with a wave packet travels is called group 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.

Is group velocity equal to phase velocity?

The phase velocity is: vp = ω/k. The function ω(k), which gives ω as a function of k, is known as the dispersion relation. If ω is directly proportional to k, then the group velocity is exactly equal to the phase velocity.

What is the difference between a group velocity and phase velocity of an EM wave?

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. Phase velocity is defined as the velocity of a single wave.

Is phase velocity and wave velocity same?

conceptually is there any difference between phase velocity and wave velocity? No, there is no difference. a string. For a wave traveling in the that means kx -ωt constant.

What exactly is phase velocity?

The phase velocity is defined as the velocity for a single-wavelength wave, whereas the group velocity is defined as the velocity for a packet of waves in which the waves vary in wavelength.

Can group velocity exceed c?

Sommerfeld pointed out that while it is true that both the phase and the group velocities in media can in fact exceed c, the front velocity, defined as the velocity of a discontinuous jump in the initial wave amplitude from zero to a finite value, cannot exceed c.

Why can group velocity be greater than c?

But teachers often say that the “group velocity”–the speed of a wave pulse, like a single traveling “wiggle” on a stretched rope–cannot be larger than c because it represents the speed of a physical signal. The explanation is that the central piece of the pulse is attenuated more than the earliest piece.

Is phase velocity exceeds the velocity of light explain?

Remember that the phase velocity is just the apparent speed at which the humps of wave appear to travel. However, the waves themselves are not travelling faster than light.

What is the difference between phase and group velocity?

The group velocity is often equal to the information velocity, but that is not always true. Also, the group velocity is not always less than the phase velocity. The group velocity can be much, much less than c (~10 m/s), equal to c, greater than c, or even negative.

What does phase velocity mean?

Phase velocity. The phase velocity of a wave is the rate at which the phase of the wave propagates in space.

What is a velocity group?

Group velocity. The group velocity of a wave is the velocity with which the overall shape of the wave’s amplitudes—known as the modulation or envelope of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water,…

What is group velocity?

The group velocity of a wave is the velocity with which the overall shape of the wave’s amplitudes—known as the modulation or envelope of the wave—propagates through space.