Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
Question
Book Icon
Chapter 6, Problem 47E

(a)

To determine

To calculate:

The phase and group velocities.

(b)

To determine

Spread of the wave as it travels.

Blurred answer
Students have asked these similar questions
The phase velocity v of gravity waves in a liquid of depth h is given by the formula v = tanh kh, k where g is the acceleration of free fall and k = 2w/2 is the wavenumber, a being the wavelength. Sketch the dispersion relation for such waves, and show that the group velocity is always between v2 and v. Find the phase and group velocities for gravity waves of frequency 1 Hz in a liquid of depth 0.1 m.
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.
Q.18. Verify the statement in the text that, if the phase velocity is the same for all wavelengths of a certain wave phenomenon (that is, there is no dispersion), the group and phase velocities are the same?
Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning