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 one 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. n₁ n₂=6 aligned 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 -600 & =6 aligned Given that fundamental frequency Dividing Eq. (i) by Eq. (ii), we get 1 2 l T^ m 1 2 l T m = 606 600 array ll or & T^ T =(1.01) or & T^ T =(1.02) % or & T^ =T(1.02) array Increase in tension aligned T^ & =T 1.02-T & =(0.02 T) Hence, T^ =0.02 aligned