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Question

If $$n_{1}, n_{2}, n_{3}$$ be the frequency of the segments of a stretched string, then the frequency $$n$$ of the string itself in terms of $$n_{1}, n_{2}$$ and $$n_{3}$$ is


A
(n1n2+n2n3+n1n3)n1n2n3
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B
(n1n2+n3n1)n1n2n3
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C
n1n2n3(n1n2+n3n1)
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D
n1n2n3(n1n2+n2n3+n3n1)
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Solution

The correct option is C $$\dfrac{\mathrm{n}_{1}\mathrm{n}_{2}\mathrm{n}_{3}}{(\mathrm{n}_{1}\mathrm{n}_{2}+\mathrm{n}_{2}\mathrm{n}_{3}+\mathrm{n}_{3}\mathrm{n}_{1})}$$
frequency $$\dfrac{1}{n}=\ \ \ \dfrac{1}{n_1}+\dfrac{1}{n_2}+\dfrac{1}{n_3}$$
$$\Rightarrow \dfrac{1}{n}=\ \ \dfrac{n_1n_2+n_2n_3+n_3n_1}{n_1n_2n_3}$$
$$\Rightarrow n = \dfrac{n_1n_2n_3}{n_1n_2+n_2n_3+n_3n_1}$$

Physics

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