Q. If $n_{1},n_{2},n_{3}\ldots.$ are the frequencies of segments of a stretched string, the frequency $n$ of the string is given by
A) $n = n_{1} + n_{2} + n_{3} + \ \ldots.$
B) $n = \sqrt{n_{1} \times n_{2} \times n_{3} \times \ldots}$
C) $\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}} + \ \ldots$
D) None of these
Explanation
(c) For a vibrating string
$n_{1}l_{1} = n_{2}l_{2} = n_{3}l_{3}\ldots. = constant = k(say) = nl$
Also $l_{1} + l_{2} + l_{3} + l_{4} + \ \ldots.. = 1$
$\frac{k}{n_{1}} + \frac{k}{n_{2}} + \frac{k}{n_{3}} + \frac{k}{n_{4}} + \ \ldots = \frac{k}{n} \Rightarrow \frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}} + \ \ldots.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.