Two open organ pipes of fundamental frequencies $n_{1} and n_{2}$ are joined in series. The fundamental frequency of the new pipe so obtained will be :

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$(n_{1} + n_{2})$

$\frac{n_{1} n_{2}}{n_{1} + n_{2}}$

$\sqrt{{n_{1}}^{2} + {n_{2}}^{2}}$

$\frac{n_{1} + n_{2}}{2}$

answer is C.

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Detailed Solution

$n_{1} = \frac{V}{2 L_{1}} n_{2} = \frac{V}{2 L_{2}}$

Both open pipes joined

$n = \frac{V}{2 (L_{1} + L_{2})} = \frac{1}{\frac{2 L_{1}}{V} + \frac{2 L_{2}}{V}} = \frac{1}{\frac{1}{n_{1}} + \frac{1}{n_{2}}} = \frac{n_{1} n_{2}}{n_{1} + n_{2}}$

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