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The frequency of transverse vibrations in a stretched string is $100 Hz$ . If the tension is increased to two times and the length is reduced to one-fourth the original values, the frequency of vibration will be

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$1600 Hz$

$400 \sqrt{2} Hz$

$25 Hz$

$200 Hz$

answer is C.

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Detailed Solution

Frequency $n_{1} = 100 Hz$

Tension $T_{1} = T$

Tension $T_{2} = 2 T$

Length $l_{1} = l$

Length $l_{2} = \frac{l}{4}$

$\frac{n_{1}}{n_{2}} = \frac{l_{2}}{l_{1}} \sqrt{\frac{T_{1}}{T_{2}}}$

$\frac{100}{n_{2}} = \frac{\frac{l}{4}}{l} \sqrt{\frac{T}{2 T}}$

$\frac{100}{n_{2}} = \frac{1}{4} \sqrt{\frac{1}{2}}$

$n_{2} = 400 \sqrt{2} H z$

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