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Q11CQ

Expert-verifiedFound in: Page 223

Book edition
2nd Edition

Author(s)
Randy Harris

Pages
633 pages

ISBN
9780805303087

**The diagram below plots ω(k) versus wave number for a particular phenomenon. How do the phase and group velocities compare, and do the answer depend on the central value of k under consideration? Explain.**

The values of phase and group velocities depend on the central value of k under consideration.

Group velocity is defined as the velocity of the whole envelope of a wave in space.

Phase velocity is defined as the velocity of a phase or part of a wave in space.

For small (central) values of k, the slope of the curve, or tangent line, dω/dk is tany, and therefore the slope of a line from the origin, *ω/k* is relatively large. That is, the group velocity is smaller than the phase velocity. When the central value of k is large, these two quantities are equal, and so are the phase and group velocities.

Hence, the values of phase and group velocities depend on the central value of k under consideration.

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