A guitar string of length 90,cm vibrates with a fundamental frequency of 120,Hz. length of string pr

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14.Waves and Sound

easy

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 $...........cm$.

A

$60$

B

$59$

C

$58$

D

$57$

(JEE MAIN-2023)

Solution

$f =\frac{ nv }{2 \ell}, \text { for fundamental mode } n =1$

$f =\frac{ v }{2 \ell}$

$f \propto \frac{1}{\ell}$

$\frac{ f _1}{ f _2}=\frac{\ell_2}{\ell_1}$

$\frac{120}{180}=\frac{\ell_2}{90}$

$\ell_2=60\,cm$

Standard 11

Physics

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(JEE MAIN-2023)