To increase the frequency of a stretched stri | vedclass

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(B) The fundamental frequency $n$ of a stretched string is given by the formula $n = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $

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$16$

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(B) The fundamental frequency $n$ of a stretched string is given by the formula $n = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the linear mass density.Since $L$ and $\mu$ are constant,we have $n \propto \sqrt{T}$.Let the initial frequency be $n_1 = 100 \ Hz$ and the final frequency be $n_2 = 400 \ Hz$.Then,$\frac{n_2}{n_1} = \sqrt{\frac{T_2}{T_1}}$.Substituting the values: $\frac{400}{100} = \sqrt{\frac{T_2}{T_1}} \implies 4 = \sqrt{\frac{T_2}{T_1}}$.Squaring both sides,we get $\frac{T_2}{T_1} = 4^2 = 16$.Therefore,the tension must be increased by $16$ times.

To increase the frequency of a stretched string from $100 \ Hz$ to $400 \ Hz$,the tension in the string has to be changed by how many times?

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