n waves are produced on a string in 1 s. Whe | vedclass

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(B) The frequency of vibration of a string is given by the formula:$f = \frac{1}{2L} \sqrt{\frac{T}{m}}$where $T$ is the tension,$L$ is the length,and

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$\frac{n}{2}$

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(B) The frequency of vibration of a string is given by the formula:$f = \frac{1}{2L} \sqrt{\frac{T}{m}}$where $T$ is the tension,$L$ is the length,and $m$ is the mass per unit length.Since $m = \pi r^2 \rho$ (where $r$ is the radius and $\rho$ is the density),the frequency $n$ is:$n = \frac{1}{2L} \sqrt{\frac{T}{\pi r^2 \rho}} = \frac{1}{2Lr} \sqrt{\frac{T}{\pi \rho}}$From this expression,we see that $n \propto \frac{1}{r}$ when $T$,$L$,and $\rho$ are constant.If the radius is doubled $(r' = 2r)$,the new frequency $n'$ becomes:$\frac{n'}{n} = \frac{r}{r'} = \frac{r}{2r} = \frac{1}{2}$Therefore,$n' = \frac{n}{2}$.

$n$ waves are produced on a string in $1 \ s$. When the radius of the string is doubled,keeping the tension the same,the number of waves produced in $1 \ s$ for the same harmonic will be

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