When a string is divided into three segments | vedclass

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Question

$V=\frac{1}{2 l} \sqrt{\frac{T}{m}}$

$v_{1} l_{1}=v_{2} l_{2}=v_{3} l_{3}=k$

from eq. $(1)$

$l_{1}=\frac{k}{v_{1}}, l_{2}=\frac{k}{v_{2}}, l_

Vedclass · Accepted Answer

$\frac{1}{v} = \frac{1}{{{v_1}}} + \frac{1}{{{v_2}}} + \frac{1}{{{v_3}}}$

Vedclass · Answer

$V=\frac{1}{2 l} \sqrt{\frac{T}{m}}$

$v_{1} l_{1}=v_{2} l_{2}=v_{3} l_{3}=k$

from eq. $(1)$

$l_{1}=\frac{k}{v_{1}}, l_{2}=\frac{k}{v_{2}}, l_{3}=\frac{k}{v_{3}}$

original length

$l=\frac{k}{v}$

Here$, l=l_{1}+l_{2}+l_{3}$

$\frac{k}{v}=\frac{k_{1}}{v_{1}}+\frac{k_{2}}{v_{2}}+\frac{k_{3}}{v_{3}}$

$\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}$

When a string is divided into three segments of length $l_1,\,l_2$ and $l_3,$ the fundamental frequencies of these three segments are $v_1,\,v_2$ and $v_3$ respectively. The original fundamental frequency $(v)$ of the string is

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