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

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(2) 0.02. Given: 
u=600 Hz on both wires, and 6 beats per second wanted. Idea: on a string 
u∝√T, so a small fractional change in tension makes half as large a fractional change in frequency. Taking logarithms and differentiating, (Δ
u)/u=1/2(Δ T)/T. Δ
u=6 Hz, so (Δ
u)/u=6/(600)=0.01. (Δ T)/T=2×0.01. (Δ T)/T=0.02.

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

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