Question

Two stretched wires of same length, diameter and same material are in unison. The tension in one is increased by $2\%$ and $2$ beats per second are heard. What was the frequency of the note produced when they were in unison

• A. $100Hz$
• B. $200Hz$
• C. $500Hz$
• D. $400Hz$

Answer 1

The correct option is B $200Hz$

$\begin{array}{c}f=\frac{v}{2l}=\frac{1}{2l}\sqrt{\frac{T}{\mu }}\\ T=T+\frac{2}{100}T\\ \frac{df}{f}\times 100=\frac{1}{2}\times \left(\frac{dt}{T}\times 100\right)\\ =1010\\ \Rightarrow dF=\frac{f}{100}\\ f=100\left(dF\right)\\ =100\left(2\right)\\ =200Hz\end{array}$

$\therefore$ Option $B$ is correct .