Q. A wire under tension vibrates with a fundamental frequency of 600 Hz. If the length of the wire is doubled, the radius is halved and the wire is made to vibrate under one-ninth the tension. Then the fundamental frequency will become
A) 400 Hz
B) 600 Hz
C) 300 Hz
D) 200 Hz
Explanation
(d) $fundamental\ frequency\ f = \frac{1}{2r\iota}\sqrt{\frac{T}{\pi\rho}}$
$\therefore\ \frac{f_{1}}{f_{2}} = \frac{\iota_{2}}{\iota_{1}} \times \frac{r_{2}}{r_{1}}$
$\frac{600}{f_{2}} = \frac{2}{1} \times \frac{1}{2}\ \times \sqrt{\frac{T}{T/9}}$
$f_{2} = 200Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.