Question

The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant, its length must be increased by:

• A. $30\%$
• B. $20\%$
• C. $69\%$
• D. $\sqrt{69}\%$

Answer 1

The correct option is A $30\%$

$\begin{array}{c}n\propto \frac{\sqrt{T}}{l}\\ \Rightarrow l\propto \sqrt{T}\left(Asn=cons\tan t\right)\\ \Rightarrow \frac{l_2}{l_1}=\sqrt{\frac{T_2}{T_1}}=l_1\sqrt{\frac{169}{100}}\\ \Rightarrow l_2=1.3l_1=l_1+30of{l}_1\end{array}$

Hence, Option $A$ is correct.