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  4. If the vibration of a string are to be increased by a factor of 2. Then tension in the string must be made :

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Q. If the vibration of a string are to be increased by a factor of 2. Then tension in the string must be made :

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Solution:

Here, initial vibration $ {{n}_{1}}=n $ Final vibration $ {{n}_{2}}=2n $ Initial tension $ T=T $ The vibration of frequency of string is $ n=\frac{1}{2l}\frac{\sqrt{T}}{m}\propto \sqrt{T} $ Hence, $ \frac{{{n}_{1}}}{{{n}_{2}}}=\frac{\sqrt{{{T}_{1}}}}{{{T}_{2}}} $ or $ \frac{n}{2n}\frac{\sqrt{{{T}_{1}}}}{{{T}_{2}}} $ or $ \frac{{{T}_{1}}}{{{T}_{2}}}=\frac{1}{4} $ or $ {{T}_{2}}=4{{T}_{1}} $