Question

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 wires which will lead to the occurence of 6 beats per second when both the wires oscillate together would be

Answer 1

We want one of the wires to alter the frequency by 6 Hz  = 0.01 or 1%

   frequency f = √[ T /μ ]
relative errors:    Δf/f = 1/2 *  ΔT/T  + 1/2 * Δμ /μ

Δf / f = 0.01   =>   ΔT/T = 0.02       as  μ = constant.
The fractional increase 0.02 or  2%

Answer 2

V= frequency.

 V=1/2L (T/U) ^1/2. (formula) Now, delta v/v=1/2delta T/T          delta T/T=2delta v/v.                          2*6/600.                                           =0.02