Q. The frequency of transverse vibrations in a stretched string is $200\ Hz.$ If the tension is increased four times and the length is reduced to one-fourth the original value, the frequency of vibration will be
A) $25\ Hz$
B) $200\ Hz$
C) $400\ Hz$
D) $1600\ Hz$
Explanation
(d) $n = \frac{1}{2l}\sqrt{\frac{T}{m}} \Rightarrow \frac{n_{1}}{n_{2}} = \frac{l_{2}}{l_{1}}\sqrt{\frac{T_{1}}{T_{2}}} = \frac{1}{4}\sqrt{\frac{1}{4}} = \frac{1}{8}$
$\Rightarrow n_{2} = 8n_{1} = 8 \times 200 = 1600Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.