A) \[3T\]
B) \[\frac{T}{9}\]
C) \[\frac{T}{\sqrt{3}}\]
D) \[9T\]
Correct Answer: D
Solution :
The frequency of a string \[f=\frac{1}{2\,l}\,\sqrt{\frac{T}{\mu }}\] where \[\mu \] is mass per unit length of strings and T is tension in the string. \[\therefore \] \[f\propto \sqrt{T}\,\,\,\,\Rightarrow \,\,\,\,T\propto {{f}^{2}}\] \[\Rightarrow \] \[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{f}_{2}}}{{{f}_{1}}} \right)}^{2}}\] Given, \[{{f}_{1}}=f,\,\,\,\,\,{{f}_{2}}=3f,\,\,\,\,{{T}_{1}}=T\] \[\therefore \] \[\frac{{{T}_{2}}}{T}={{\left( \frac{3f}{f} \right)}^{2}}\] \[\Rightarrow \] \[{{T}_{2}}=9\,T\]
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