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.
A real wave function is defined on the half-axis: [0≤x≤00) as y(x) = A(x/xo)e-x/xo where xo is a given constant with the dimension of length. a) Plot this function in the dimensionless variables and find the constant A. b) Present the normalized wave function in the dimensional variables. Hint: introduce the dimensionless variables = x/xo and Y(5) = Y(5)/A.
TTX Consider the wave function V(x, t) = A(cos (A)) e-jot for – 1
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