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530_Physics ProblemsTechnical Physics

# 530_Physics ProblemsTechnical Physics - 532 Superposition...

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532 Superposition and Standing Waves Section 18.3 Standing Waves in a String Fixed at Both Ends P18.19 L = 30 0 . m; µ = × 9 00 10 3 . kg m; T = 20 0 . N ; f v L 1 2 = where v T = F H G I K J = µ 1 2 47 1 . m s so f 1 47 1 60 0 0 786 = = . . . Hz f f 2 1 2 1 57 = = . Hz f f 3 1 3 2 36 = = . Hz f f 4 1 4 3 14 = = . Hz *P18.20 The tension in the string is T = = 4 9 8 39 2 kg m s N 2 b g e j . . Its linear density is µ = = × = × m L 8 10 1 6 10 3 3 kg 5 m kg m . and the wave speed on the string is v T = = × = µ 39 2 10 156 5 3 . . N 1.6 kg m m s In its fundamental mode of vibration, we have λ = = = 2 2 5 10 L m m a f Thus, f v = = = λ 156 5 10 15 7 . . m s m Hz P18.21 (a) Let n be the number of nodes in the standing wave resulting from the 25.0-kg mass. Then n + 1 is the number of nodes for the standing wave resulting from the 16.0-kg mass. For
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