The fundamental frequency of a sonometer wire | vedclass

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(D) The fundamental frequency $n$ of a sonometer wire is given by the formula:$n = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$where $T$ is the tension,$l$ is t

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$\frac{n}{2\sqrt{2}}$

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(D) The fundamental frequency $n$ of a sonometer wire is given by the formula:$n = \frac{1}{2l} \sqrt{\frac{T}{\mu}}$where $T$ is the tension,$l$ is the length,and $\mu$ is the linear mass density.Since $\mu = \pi r^2 ho$ (where $r$ is the radius and $ho$ is the density of the material),the formula becomes:$n = \frac{1}{2l} \sqrt{\frac{T}{\pi r^2 ho}} = \frac{1}{2l} \frac{1}{r} \sqrt{\frac{T}{\pi ho}}$This implies $n \propto \frac{\sqrt{T}}{r}$.Given that the new radius $r_2 = 2r_1$ and the new tension $T_2 = \frac{T_1}{2}$,the ratio of the new frequency $n_2$ to the original frequency $n_1$ is:$\frac{n_2}{n_1} = \frac{r_1}{r_2} \sqrt{\frac{T_2}{T_1}} = \frac{r_1}{2r_1} \sqrt{\frac{T_1/2}{T_1}} = \frac{1}{2} 	imes \sqrt{\frac{1}{2}} = \frac{1}{2\sqrt{2}}$.Therefore,the new frequency $n_2 = \frac{n}{2\sqrt{2}}$.

The fundamental frequency of a sonometer wire is $n$. If its radius is doubled and its tension becomes half,while the material of the wire remains the same,the new fundamental frequency will be

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