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NEET - 2012

When a string is divided into three segments of lengths  the fundamental frequencies of these three segments are  respectively. The original fundamental frequency (v) of the string is

(a) $\sqrt{v}=\sqrt{{v}_{1}}+\sqrt{{v}_{2}}+\sqrt{{v}_{3}}$

(b) $v={v}_{1}+{v}_{2}+{v}_{3}$

(c) $\frac{1}{v}=\frac{1}{{v}_{1}}+\frac{1}{{v}_{2}}+\frac{1}{{v}_{3}}$

(d) $\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{{v}_{1}}}+\frac{1}{\sqrt{{v}_{2}}}+\frac{1}{\sqrt{{v}_{3}}}$

The fundamental frequency of string

$v=\frac{1}{2l}\sqrt{\frac{T}{m}}$

...(i)

From Eq. (i)

${l}_{1}=\frac{k}{{v}_{1}},{l}_{2}=\frac{k}{{v}_{2}},{l}_{3}=\frac{k}{{v}_{3}}$

Original length

$l=\frac{k}{v}$

Here,     $l={l}_{1}+{l}_{2}+{l}_{3}$

$\frac{k}{v}=\frac{k}{{v}_{1}}+\frac{k}{{v}_{2}}+\frac{k}{{v}_{3}}$

$\frac{1}{v}=\frac{1}{{v}_{1}}+\frac{1}{{v}_{2}}+\frac{k}{{v}_{3}}$

Difficulty Level:

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