A segment of wire vibrates with a fundamental | vedclass

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(A) The fundamental frequency $f$ of a vibrating wire is given by the formula: $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\

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$36 ~kg-wt$

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(A) The fundamental frequency $f$ of a vibrating wire is given by the formula: $f = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Since the wire is the same,$L$ and $\mu$ are constant,so $f \propto \sqrt{T}$.Therefore,we can write the ratio: $\frac{f_2}{f_1} = \sqrt{\frac{T_2}{T_1}}$.Given $f_1 = 450 ~Hz$,$T_1 = 9 ~kg-wt$,and $f_2 = 900 ~Hz$.Substituting the values: $\frac{900}{450} = \sqrt{\frac{T_2}{9}}$.$2 = \sqrt{\frac{T_2}{9}}$.Squaring both sides: $4 = \frac{T_2}{9}$.$T_2 = 4 	imes 9 = 36 ~kg-wt$.

$A$ segment of wire vibrates with a fundamental frequency of $450 ~Hz$ under a tension of $9 ~kg-wt$. The tension at which the fundamental frequency of the same wire becomes $900 ~Hz$ is

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