Question

In a resonance tube experiment, $3^{\text{rd }}$ resonance occurs at $111cm$ and $5^{\text{th }}$ resonance occurs at $200cm$ . Find the end correction (in $cm$ ) is $\alpha$ . Write the value of $100\alpha$ .

Answer 1

Answer: 25

In the resonance tube, for $3^{rd}$ resonance,
$\frac{5\lambda }{4}=l_1+e$ .....(i)
For $5^{\text{th}}$ resonance,
$\frac{9\lambda }{4}=l_2+e$ .....(ii)
From (i) and (ii), $\lambda =l_2-l_1=200-111=89cm$
From (i), end correction $e=\frac{5\lambda }{4}-l_1=\frac{5}{4}\times 89-111$
$\Rightarrow e=0.25cm=\alpha 100\alpha =25$