Two identical piano wires have a fundamental frequency of 600 cycle per second when kept under the same tension. What fractional increase in the tension of wires will lead to the occurrence of 6 beats per second when both wires vibrate simultaneously?

Step-by-step solution

Beats per second when both the wires vibrate simultaneously n 1 ± n 2 = 6 or 1 2 l ⁡ T m ± 1 2 l ⁡ T ' m = 6 or 1 2 l ⁡ T ' m - 1 2 l ⁡ T m = 6 or 1 2 l ⁡ T ' m - 6 0 0 = 6 ...(i) Given that fundamental frequency 1 2 l T m = 600 Dividing Eq.(i) by Eq. (ii), we get 1 2 l ⁡ T ' m 1 2 l ⁡ T m = 6 0 6 6 0 0 Or T ' T = 1.01 Or T ⁡ ′ T ⁡ = 1 . 0 2 % Or T ' = T ( 1 . 02 ) Increase in tension Δ T ' = ( T × 1 . 02 ) – T = 0 . 02 T Hence, Δ T ' = 0 . 02