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528_Physics ProblemsTechnical Physics

528_Physics ProblemsTechnical Physics - 530 Superposition...

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530 Superposition and Standing Waves Section 18.2 Standing Waves P18.13 y x t A kx t = = 1 50 0 400 200 2 0 . sin . cos sin cos m a f a f a f ω Therefore, k = = 2 0 400 π λ . rad m λ π = = 2 0 400 15 7 . . rad m m and ω π = 2 f so f = = = ω π π 2 200 2 31 8 rad s rad Hz . The speed of waves in the medium is v f f k = = = = = λ λ π π ω 2 2 200 0 400 500 rad s rad m m s . P18.14 y x t = F H G I K J 0 030 0 2 40 . cos cos m a f (a) nodes occur where y = 0: x n 2 2 1 2 = + a f π so x n = + = 2 1 3 5 a f π π π π , , , . (b) y max . cos . . = F H G I K J = 0 030 0 0 400 2 0 029 4 m m P18.15 The facing speakers produce a standing wave in the space between them, with the spacing between nodes being d v f NN m s s m = = = = λ 2 2 343 2 800 0 214 1 e j . If the speakers vibrate in phase, the point halfway between them is an antinode of pressure at a
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