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A wire of certain length under tension T vibrates at its fundamental frequency f0. The length is then decreased by 45% (new length = 0.55 of original) and the tension is increased by 21% (new tension = 1.21T). How does the new fundamental frequency compare to the original?

1. Increases by 50%
2. Increases by 100%
3. Decreases by 50%
4. Decreases by 25%

Correct answer: Increases by 100%

Solution

f = (1/2L)*sqrt(T/mu). f_new/f_old = (L_old/L_new) * sqrt(T_new/T_old) = (1/0.55) * sqrt(1.21) = (1/0.55) * 1.1 = 1.1/0.55 = 2. So the new frequency is 2 times the old frequency, meaning it increases by 100%.

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