Q. If $n_1$, $n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, the original fundamental frequency n of the string is given by :
A) $\frac{1}{n} = \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3}$
B) $\frac{1}{\sqrt{n}} = \frac{1}{\sqrt{n_1}} + \frac{1}{\sqrt{n_2}} + \frac{1}{\sqrt{n_3}}$
C) $\sqrt{n} = \sqrt{n_1} + \sqrt{n_2} + \sqrt{n_3}$
D) $n = n_1 + n_2 + n_3$
Explanation
[Solution] For the same tension and mass per length, n ∝ 1/l; since $l = l_1 + l_2 + l_3$, $\frac{1}{n} = \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3}$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.