In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of \(20.0 \,cm\) for a tuning fork of frequency \(400 \,Hz\) is used. The velocity of the sound at room temperature is \(336 \,ms ^{-1}\). The third resonance is observed when the air column has a length of ......... \(cm\)

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Correct Answer

(D) \(104\)

Step-by-step Solution

Detailed explanation

For first resonance

\(\ell_{1}+ e =\frac{\lambda}{4}\)

\(\lambda=\frac{336}{400} \times 100 \,cm =84 \,cm \Rightarrow \frac{\lambda}{4}=21 \,cm\)

\(e =21-20=1 \,cm\)

For third resonance

\(\ell_{3}+ e =\frac{5 \lambda}{4}=105 \,cm \Rightarrow \ell_{3}=104 \,cm\)

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