Q. 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) 20%
B) 30%
C) $\sqrt{69}\%$
D) 69%
Explanation
(b) $n \propto \frac{\sqrt{T}}{l} \Rightarrow l \propto \sqrt{T}\ \ \ \ \ \ \ \ \ \ \lbrack As\ n = constant\rbrack$
$\Rightarrow \frac{l_{2}}{l_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = l_{1}\sqrt{\frac{169}{100}} \Rightarrow l_{2} = 1.3l_{1} = l_{1} + 30\%$ of $l_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.