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A stretched wire of some length under a tension is vibrating with its fundamental frequency. Its length is decreased by 45% and tension is increased by 21%. Now its fundamental frequency

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increases by 100%

decreases by 50%

decreases by 25%

increases by 50%

answer is B.

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Detailed Solution

$n \propto \frac{\sqrt{T}}{l} \Rightarrow \frac{n_{2}}{n_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} x \frac{l_{1}}{l_{2}} = \sqrt{\frac{121}{100}} x \frac{100}{55} \Rightarrow \frac{11}{10} x \frac{100}{55} = 2$

$\frac{n_{2} - n_{1}}{n_{1}} x 100 = 100 %$

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