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Unformatted text preview: Physics 315: Oscillations and Waves Homework 8: Due in class on Friday, Nov. 13th 1. A uniform rope of mass per unit length and length L hangs vertically. Determine the tension T in the rope as a function of height from the bottom of the rope. Show that the time required for a transverse wave pulse to travel from the bottom to the top of the rope is 2 radicalbig L/g . 2. Demonstrate that the phase velocity of traveling waves on an infinitely long beaded string is v p = v sin( k a/ 2) ( k a/ 2) , where v = radicalbig T a/m , T is the tension in the string, a the spacing between the beads, m the mass of the beads, and k the wavenumber of the wave. What is the group velocity? 3. The number density of free electrons in the ionosphere, n e , as a function of vertical height, z , is measured by timing how long it takes a radio pulse launched vertically upward from the ground ( z = 0) to return to ground level again, after reflection by the ionosphere, as a function of the pulse frequency,...
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