Question

Three similar wires of frequency $n_{1}, n_{2} and n_{3}$ are joined to make one wire. Its frequency will be

Moderate

A

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

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

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

$\frac{1}{n^{2}} = \frac{1}{{n^{2}}_{1}} + \frac{1}{{n^{2}}_{2}} + \frac{1}{{n^{2}}_{3}}$

Solution

$n = \frac{1}{2 l} \sqrt{\frac{T}{m}} \Rightarrow n_{1} l_{1} = n_{2} l_{2} = n_{3} l_{3} = k$
$l_{1} + l_{2} + l_{3} = l \Rightarrow \frac{k}{n_{1}} + \frac{k}{n_{2}} + \frac{k}{n_{3}} = \frac{k}{n}$
$\Rightarrow \frac{1}{n} = \frac{1}{n_{1}} + \frac{1}{n_{2}} + \frac{1}{n_{3}} + . . . .$

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