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).
Both the pressure and the electric signal are measured simultaneously for various settings, and the results are tabulated. For the given set of measurements, obtain the calibration curve in the form of P = aI + b, where a and b are constants, and calculate the pressure that corresponds to a signal of 10 mA.
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.
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