MCQ

A sonometer wire of length *l* vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will

#### Options

vibrate with a frequency of 416 Hz

vibrate with a frequency of 208 Hz

vibrate with a frequency of 832 Hz

stop vibrating.

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#### Solution

vibrate with a frequency of 208 Hz

According to the relation of the fundamental frequency of a string

\[\nu = \frac{1}{2l}\sqrt{\frac{F}{\mu}}\]

where

*l* is the length of the string

*F *is the tension

*μ is the *linear mass density

We know that ν_{1} = 416 Hz, *l*_{1} = *l *and *l*_{2} = 2*l**.\[v_1 \propto \frac{1}{l_1}\]\[ v_1 l_1 = v_2 l_2 \]\[\left( 416 \right)l = v_2 \left( 2l \right)\]\[ v_2 = 208 Hz\] *

Concept: The Speed of a Travelling Wave

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