Question

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

• A. $0.02$
• B. $0.03$
• C. $0.04$
• D. $0.01$

Answer 1

The correct option is A $0.02$

Frequency $\nu =\frac{v}{2L}$

where $v=\sqrt{\frac{T}{\mu }}$

$⟹$ $\nu =\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

Thus fractional change in frequency $\frac{\Delta \nu }{\nu }=\frac{1}{2}\frac{\Delta T}{T}$

Given : $\Delta \nu =6$, $\nu =600Hz$

$\therefore$ $\frac{6}{600}=\frac{1}{2}\frac{\Delta T}{T}$

$⟹$ $\frac{\Delta T}{T}=2\times 0.01=0.02$