A string is cut into three parts, having fundamental frequencies n1, n2 and n3 respectively. Then original fundamental frequency 'n' of total string is related by the expression as (other quantities are identical)

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$n = n_{1} + n_{2} + n_{3}$

$n = n_{1} \times n_{2} \times n_{3}$

$n = \frac{n_{1} + n_{2} + n_{3}}{3}$

$\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$

answer is A.

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Detailed Solution

$l = l_{1} + l_{2} + l_{3}$
$n = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$
$l \propto \frac{1}{n}$
$\frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}}$

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