Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 6, Problem 46E

(a)

To determine

To sketch:

Group velocity versus wave number.

(b)

To determine

Group velocity and wavelength

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The angular frequency of the surface waves in a liquid is given in terms of the wave number k by w = Vgk +Tk³/p, where g is the acceleration due to gravity, p is the density of the liquid, and T is the surface tension (which gives an upward force on an element of the surface liquid). Find the phase and group velocities for the limiting cases when the surface waves have: (a) very large wavelengths and (b) very small wavelengths.
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