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  4. The string of a violin has a frequency of 440 cps. If the violin string is shortened by one fifth, its frequency will be changed to

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Q. The string of a violin has a frequency of $440 \,cps$. If the violin string is shortened by one fifth, its frequency will be changed to

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Solution:

Fundamental frequency $=440\, cps =\frac{v}{2 l}$
If $l$ is made one fifth $\frac{v}{2 \times l / 5}$ or $\frac{5 v}{2 l}$
Since $\frac{v}{2 l}=440$
$5 \frac{v}{2 l}=5 \times 440=2200$