Q. If $n_{1},n_{2}\ and\ n_{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency n of the string is give 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
(a) As $n \propto \frac{1}{l}\ and\ l = l_{1} + l_{2} + l_{3}$
$\therefore\ \ \ \frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.