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A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be ………..cm.

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answer is 60.

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Detailed Solution

$n_{0} = \frac{1}{2 l} \sqrt{\frac{T}{μ}}$

$\Rightarrow n_{1} l_{1} = n_{2} l_{2}$

$\Rightarrow (120) (90) = (180) l_{2}$

$\Rightarrow l_{2} = 60 cm$

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