Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 6, Problem 45E
To determine

To Calculate:The phase and group velocities of a wave

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7.29 The speed of propagation of a surface wave in a liquid of depth much greater than λ is given by V= gλ + 2TT βλ 2TTY where g = acceleration of gravity, λ = wavelength, p = density, Y = surface tension. Compute the group velocity of a pulse in the long wavelength limit (these are called gravity waves).
Find the phase velocity and group velocity for the following two wave-forms (x and t are measured in SI units) (i) 1(x,t) = cos(4t - 2x) + cos(8t- 4.r). (ii) 2(x,t) Does these waveforms satisfy the wave equation %3D = cos(8t- 6a) + cos (4t – 4.x). %3D v² Ət? where v is a constant independent of frequency. Explain.
For vibrational states, the Boltzmann equation can be written as = exp(-AE/kT) where N, and N, are the populations of the lower and higher energy states, respectively, AE is the energy difference between the states, k is Boltzmann's constant, and Tis the temperature in kelvins. For temperatures of 20°C and 40°C, cakulate the ratios of the intensities of the anti-Stokes and Stokes lines for CCI, at (a) 218 cm-, (b) 459 cm", (c) 790 cm-!. For each temperature and Raman shift, calculate how much more intense the Stokes line is compared to the anti-Stokes line.
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