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

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Four times

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(C) The frequency of vibration of a stretched string is given by the formula $n = \frac{1}{2L} \sqrt{\frac{T}{\mu}}$,where $n$ is the frequency,$L$ is the length,$T$ is the tension,and $\mu$ is the linear mass density.From this relation,we can see that $n \propto \sqrt{T}$.If the frequency is increased by a factor of two,the new frequency $n' = 2n$.Therefore,$\frac{n'}{n} = \frac{\sqrt{T'}}{\sqrt{T}} = 2$.Squaring both sides,we get $\frac{T'}{T} = 4$,which implies $T' = 4T$.Thus,the tension must be made four times the original tension.

If the frequency of vibrations of a string is to be increased by a factor of two,then the tension in the string must be made:

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