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String Fixed at Both Ends

A sitar wire ...

Question

A sitar wire vibrates with frequency of $330$ vibrations per second. If its length is increased three times and tension is increased four times then the frequency of the wire will be

A

110 H z

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B

220 H z

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C

330 H z

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D

440 H z

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Solution

The correct option is A $220 H z$
Frequency $f = \frac{1}{2 L} \sqrt{(T / m)}$
The new value of the frequency $f^{'}$ will be $2 / 3$ times $f$ .
$f^{'} = \frac{1}{6 L} \sqrt{(4 T / m))}$
$f^{'} = 330 \times 2 / 3 = 220 H z$

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