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Phys 2214 Assignment 5 2011

# Phys 2214 Assignment 5 2011 - TA's Name Section Your Name...

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TA's Name:_____________________________________Section: ____ Your Name: ____________________________________ Physics 2214, Fall 2011 1 Cornell University Physics 2214 Assignment 5 Concepts: Energy and Power in waves Reflection and Transmission of waves Electromagnetic waves Reading: Y&F, Vol. 1, Chapters 15 & 16; Vol. 2, Chapter 21; Lecture notes Assignment: Due in second section meeting of the week of October 17. 1. Optical standing waves in a laser. A He-Ne laser can be made by placing a plasma tube filled with a mixture of the gases in an optical resonant cavity formed by two highly reflecting flat mirrors separated by a distance L. For certain values of the light wavelength, light waves reflected from the mirrors interfere constructively to form standing waves. Light emitted by the tube at the standing wave wavelengths will thus build up by reflection to produce a very strong optical field within the cavity. This strong optical field will stimulate more gas atoms in the tube to emit light at the same frequency and in phase with the stimulating light, in a process called stimulated emission, leading to lasing. (a) What are the standing wave frequencies of the optical cavity, in terms of the mirror separation L and the speed of light c? (b) Suppose that the plasma tube emits light centered at a frequency f 0 = 5 x 10 14 Hz. The spectral width f is such that all standing wave modes within 1 x 10 9 Hz of f 0 will be excited by the plasma tube. (i) How many modes will be excited if the length L=0.5 m? (ii) What is the largest value of L such that only one standing wave mode of the cavity will be excited? 2. Degrees of freedom. Using a small speaker, we broadcast a sinusoidal sound wave into an air-filled pipe of length L that is open at both ends. As we vary the frequency of the sound wave, we find that some frequencies sound much louder to us than others. (a) Sketch the maximum displacement s m (x) versus x for the three standing wave modes of lowest frequency. (b) For each mode at a given time t, are all the molecules moving in the same direction, or do molecules in different segments of the pipe move in opposite

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TA's Name:_____________________________________Section: ____ Your Name: ____________________________________ Physics 2214, Fall 2011 2 Cornell University directions? Pick one time t in your diagrams of part (a), and draw arrows indicating the direction of molecule motion in each segment.
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