Hi guys does anyone know the difference in phase velocity and group velocity?

Question

owlfred · Answer

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anonymous · Answer

Usually a wave has its own phase(angle)
the rate of change of that phase when wave is propagated is PHASE VELOCITY

GROUP VELOCITY of a wave is the velocity with which the overall shape of the wave's amplitudes propagates through space

in attachment u could see it clearly...
RED DOT SHOWS PHASE VELOCITY
GREEN DOT SHOWS THE GROUP VELOCITY

anonymous · Answer

So which is the actual velocity of the wave and what is the significance of each velocity

anonymous · Answer

Phase velocity is actual velocity of an unmodulated wave

Group velocity comes into scene when the wave(msg signal) is modulated with another wave(carrier signal) of higher freq....

consider the amplitude modulated wave(in attachment), the high frequency wave forms the envelope of the low frequency wave........

here the velocity determined with respect to envelope is phase velocity

similarly the velocity of the carrier signal in modulated wave is group velocity

anonymous · Answer

Phase velocity refers to the the velocity of individual de-Broglie wave. It is always more than the velocity of light.
Group velocity is the velocity of the group of waves ie wave packet is called group velocity & its velocity is equal to the velocity of material particle with which the wave packet is associated.

anonymous · Answer

The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.

The group velocity of the wave is the rate that changes in amplitude (the envelope of the wave) will propagate.

In a dispersive medium, the phase velocity varies with frequency and is not necessarily the same as the group velocity of the wave.