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Unformatted text preview: PHYS-1200 PHYSICS II SPRING 2005 HOMEWORK SOLUTIONS CLASS 16. 16.30, 16.42, 16.84, 17.41, 17.111; Q17.09, Q17.10 16.30. According to equation 17-39 on page 384 of the textbook, the amplitude of the resultant wave is given by: y m = 2 y m cos . If y m = 1.5 y m , we have, 1.5 y m = 2 y m cos , or cos = 0.75. Then, = 41.4, and = 82.8 In radians, = 82.8 / 180 = 1.45 rad Since one wavelength corresponds to a phase shift of 2 , this difference, in wavelengths is, = 1.45/2 = 0.231 wavelengths 16.42. The string will be flat twice each period, so T = 2(0.50 s) = 1.0 s. Then, = vT = (10 cm/s)(1.0 s) = 10 cm = 0.10 m 16.84. Since the two waves are given as cosines, they can be combined with the identity, cos + cos = 2 cos( + )cos( ) Then the formula for the standing wave is, y = y 1 + y 2 = [2 y m cos kx ] cos t y = [2(0.050) cos x ] cos 4 t = [(0.10) cos x ] cos 4 t a) For a node the amplitude must be zero. That occurs when For a node the amplitude must be zero....
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This note was uploaded on 09/17/2008 for the course PHYS 1200 taught by Professor Stoler during the Spring '06 term at Rensselaer Polytechnic Institute.
- Spring '06