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534_Physics ProblemsTechnical Physics

534_Physics ProblemsTechnical Physics - 536*P18.30...

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536 Superposition and Standing Waves *P18.30 Let m V = ρ represent the mass of the copper cylinder. The original tension in the wire is T mg Vg 1 = = ρ . The water exerts a buoyant force ρ water V g 2 F H G I K J on the cylinder, to reduce the tension to T Vg V g Vg 2 2 2 = F H G I K J = F H G I K J ρ ρ ρ ρ water water . The speed of a wave on the string changes from T 1 µ to T 2 µ . The frequency changes from f v T 1 1 1 1 = = λ µ λ to f T 2 2 1 = µ λ where we assume λ = 2 L is constant. Then f f T T 2 1 2 1 2 8 92 1 00 2 8 92 = = = ρ ρ ρ water . . . f 2 300 8 42 8 92 291 = = Hz Hz . . *P18.31 Comparing y x t = 0 002 100 . sin cos m rad m rad s a f b g d i b g d i π π with y A kx t = 2 sin cos ω we find k = = 2 1 π λ π m , λ = 2 00 . m , and ω π π = = 2 100 1 f s : f = 50 0 . Hz (a) Then the distance between adjacent nodes is d NN m = = λ 2 1 00 . and on the string are L
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