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Two identical piano wires are stretched with the same tension T. Each wire has a fundamental frequency of 600 Hz. If the tension of one wire is increased slightly, what fractional increase in tension is needed so that the two wires produce 6 beats per second when sounded together?

1. 0.02
2. 0.03
3. 0.04
4. 0.01

Correct answer: 0.02

Solution

Since f ~ sqrt(T), f'/f = sqrt(T'/T). For 6 beats f' = 606 Hz, so T'/T = (606/600)^2 = 1.0201. The fractional increase in tension is about 0.02.

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