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What is the difference between group velocity and phase velocity?
What is phase velocity?
What is group velocity?
What are phase and group velocity in wave mechanics?
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6.1: Phase and Group Velocity. Phase velocity is the speed at which a point of constant phase travels as the wave propagates. 1 For a sinusoidally-varying wave, this speed is easy to quantify. To see this, consider the wave: where ω = 2πf ω = 2 π f is angular frequency, z z is position, and β β is the phase propagation constant.
Learn the definition and relation between group velocity and phase velocity of a wave packet. Find the formula, examples, and FAQs on this topic.
- Group Velocity is the velocity with which a wave packet travels.
- Phase Velocity is the velocity with which the phase of a wave packet travels.
- The condition for dispersive waves is: \(\begin{array}{l}\frac{dV_{p}}{dk}\neq 0\end{array} \)
- The condition for non-dispersive waves is: \(\begin{array}{l}\frac{dV_{p}}{dk}=0\end{array} \)
- The equation is: \(\begin{array}{l}v{g}=v{p}+k\frac{dV_{p}}{dk}\end{array} \)
Phase velocity. Frequency dispersion in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity.
The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the modulation or envelope of the wave—propagates through space.
The group velocity of a wave is the speed at which the "envelope" of the wave travels, and it is also the speed at which information is transmitted. The phase velocity of a wave is the speed at which the "phase" of the wave travels—we will clarify what this means in the lesson.
Phase and group velocity are two important and related concepts in wave mechanics. They arise in quantum mechanics in the time development of the state function for the continuous case, i.e. wave packets.
The phase velocity is not the velocity at which “stuff” is transmitted by the wave. The velocity of the stuff is called the group velocity. To have a meaningully defined group velocity, we need to have a wave that is modulated, because an unmodulated wave is an infinite sine wave that stretches off to infinity, and such an unmodulated wave ...
