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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 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
$n = n_1 + n_2 + n_3$
Detailed Solution
Total length of string $l = l_1 + l_2 + l_3$
Frequency $\propto \frac{1}{\text{length}}$
So $\frac{1}{n} = \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3}$
Frequency $\propto \frac{1}{\text{length}}$
So $\frac{1}{n} = \frac{1}{n_1} + \frac{1}{n_2} + \frac{1}{n_3}$