When a string is divided into three segments of lengths $l_{1}, l_{2}, a n d l_{3}$ , the fundamental frequencies of these three segments are $v_{1}, v_{2} a n d v_{3}$ , respectively. The original fundamental frequency (v) of the string is

\sqrt{v} = \sqrt{v_{1}} + \sqrt{v_{2}} + \sqrt{v_{3}}

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v = v_{1} + v_{2} + v_{3}

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\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}} + \frac{1}{v_{3}}

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\frac{1}{\sqrt{v}} = \frac{1}{\sqrt{v_{1}}} + \frac{1}{\sqrt{v_{2}}} + \frac{1}{\sqrt{v_{3}}}

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Solution

The correct option is C $\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}} + \frac{1}{v_{3}}$
$\begin{matrix} V = \frac{1}{2 l} \sqrt{\frac{T}{m}} v_{1} l_{1} = v_{2} l_{2} = v_{3} l_{3} = k f r o m e q . (1) l_{1} = \frac{k}{v_{1}}, l_{2} = \frac{k}{v_{2}}, l_{3} = \frac{k}{v_{3}} o r i g i n a l l e n g t h l = \frac{k}{v} H e r e, l = l_{1} + l_{2} + l_{3} \frac{k}{v} = \frac{k_{1}}{v_{1}} + \frac{k_{2}}{v_{2}} + \frac{k_{3}}{v_{3}} \frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}} + \frac{1}{v_{3}} \end{matrix}$
Hence, Option $C$ is correct .

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When a string is divided into three segments of lengths l1,l2,andl3, the fundamental frequencies of these three segments are v1,v2andv3, respectively. The original fundamental frequency (v) of the string is

The correct option is C 1v=1v1+1v2+1v3V=12l√Tmv1l1=v2l2=v3l3=kfromeq.(1)l1=kv1,l2=kv2,l3=kv3originallengthl=kvHere,l=l1+l2+l3kv=k1v1+k2v2+k3v31v=1v1+1v2+1v3Hence, Option C is correct .

When a string is divided into three segments of lengths $l_{1}, l_{2}, a n d l_{3}$ , the fundamental frequencies of these three segments are $v_{1}, v_{2} a n d v_{3}$ , respectively. The original fundamental frequency (v) of the string is