Q. In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $3/4th$ of the original length and the tension is changed. The factor by which the tension is to be changed, is
A) $3/8$
B) $2/3$
C) $8/9$
D) $9/4$
Explanation
(d) $n = \frac{1}{2l}\sqrt{\frac{T}{m}} \Rightarrow n \propto \frac{\sqrt{T}}{l} \Rightarrow \frac{T_{2}}{T_{1}} = \left( \frac{n_{2}}{n_{1}} \right)^{2}\left( \frac{l_{2}}{l_{1}} \right)^{2} = (2)^{2}\left( \frac{3}{4} \right)^{2} = \frac{9}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.