A) twice
B) four times
C) eight rimes
D) half
Correct Answer: B
Solution :
The frequency of vibration of a string is given by \[n=\frac{1}{2l}\sqrt{\frac{T}{m}}\]where \[l\]is length, T the tension and m the mass per unit length. Given, \[{{n}_{1}}=n,{{n}_{2}}=2n\] \[\therefore \] \[\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{n}{2n}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}\] \[\Rightarrow \] \[\frac{1}{4}=\frac{{{T}_{1}}}{{{T}_{2}}}\] \[\Rightarrow \] \[{{T}_{2}}=4{{T}_{1}}\] Hence, to increase n by a factor of 2 tension must increase four times.
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