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. [2023]

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Solution

Q.
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. [2023]

Ans.
(60)

$f = \frac{m v}{2 l}, for fundamental mode n = 1$

$f = \frac{v}{2 l} \Rightarrow f \propto \frac{1}{l}$

$\frac{f_{1}}{f_{2}} \propto \frac{l_{2}}{l_{1}}$

$\Rightarrow \frac{120}{180} = \frac{l_{2}}{90} \Rightarrow l_{2} = 60 cm$

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