To increase the frequency by 20 %, the tension in the string vibrating on a sonometer has to be increased by

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22%

33%

11%

44%

answer is A.

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Detailed Solution

$n \propto \sqrt{T} \Rightarrow \frac{T_{1}}{T_{2}} = \frac{{n_{2}}^{2}}{{n_{1}}^{2}}$

$\Rightarrow \frac{T_{2}}{T_{1}} = {(\frac{120}{100})}^{2} \Rightarrow \frac{T_{2}}{T_{1}} = \frac{144}{100}; \frac{T_{2}}{T_{1}} - 1 = \frac{144}{100} - 1$

So, $\frac{T_{2} - T_{1}}{T_{1}} x 100 = \frac{44}{100} x 100 = 44 %$

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