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(B) In a resonance column experiment,the frequency of the tuning fork $f$ remains constant.For the first resonance in winter,the length is $\ell_1 = 1

Vedclass · Accepted Answer

$x > 54 \ cm$

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(B) In a resonance column experiment,the frequency of the tuning fork $f$ remains constant.For the first resonance in winter,the length is $\ell_1 = 18 \ cm$. The frequency is given by $f = \frac{v}{4 \ell_1} = \frac{v}{4 	imes 18}$,where $v$ is the speed of sound in winter.For the second resonance in summer,the length is $\ell_2 = x \ cm$. The frequency is given by $f = \frac{3v'}{4 \ell_2} = \frac{3v'}{4x}$,where $v'$ is the speed of sound in summer.Equating the frequencies: $\frac{v}{4 	imes 18} = \frac{3v'}{4x}$.Solving for $x$: $x = 54 	imes \frac{v'}{v} \ cm$.Since the temperature in summer is higher than in winter,the speed of sound $v' > v$ (because $v \propto \sqrt{T}$).Therefore,$x > 54 \ cm$.

While measuring the speed of sound by performing a resonance column experiment,a student gets the first resonance condition at a column length of $18 \ cm$ during winter. Repeating the same experiment during summer,she measures the column length to be $x \ cm$ for the second resonance. Then

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