Q. Fundamental frequency of a sonometer wire is n. if the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is
A) $\frac{2n}{\sqrt{2\ }}$
B) $\frac{n}{2\sqrt{2}}$
C) $\sqrt{2}n$
D) $\frac{n}{4}$
Explanation
(d) If the length of the wire between the two bridges is 𝒍, then the frequency of vibration is
$n = \frac{1}{2\iota}\sqrt{\frac{T}{m}} = \frac{1}{2\iota}\sqrt{\frac{T}{\pi r^{2}d}}$
If the length and diameter
$\left( = \frac{radius}{2} \right)$
Of the wire are doubled keeping the tension same, the new fundamental frequency will be
$\frac{n}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.