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Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beats/s when both the wires oscillate together would be

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

Correct answer: 0.01

Solution

The beat frequency is the difference in frequencies of the two wires. If the tension in one wire is increased by a small fraction x, the new frequency becomes proportional to the square root of the tension, i.e., f' = 600√(1+x). The beat frequency is given as |f' - 600| = 6. Solving for x, we get x ≈ 0.01.

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