Length of string of a musical instrument is 90 cm and has a fundamental frequency of 120 Hz . Where

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14.Waves and Sound

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The length of the string of a musical instrument is $90 \;cm$ and has a fundamental frequency of $120 \;Hz$. Where (In $cm$) should it be pressed to produce fundamental frequency of $180 \;Hz ?$

A

$80$

B

$75$

C

$60$

D

$45$

(NEET-2020)

Solution

Frequency of stretched string

$n =\frac{1}{2 \ell} \sqrt{\frac{ T }{ m }}$

If $T$ and $m$ are constant

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

$\frac{ n ^{\prime}}{ n }=\frac{\ell}{\ell^{\prime}}$

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

$\ell=60 cm$

Standard 11

Physics

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