In a resonance tube, closed at one end by a smooth moving piston and the other end open, exhibits the first…
In a resonance tube, closed at one end by a smooth moving piston and the other end open, exhibits the first three resonance lengths of air column, $L_1$, $L_2$ and $L_3$ for the same tuning fork. Then, they are related as
$L_3 = 2L_2 = 4L_1$
$L_3 = \frac{5}{3}L_2 = 5L_1$
$(L_3 - L_2) = \left(\frac{L_2 - L_1}{2}\right)$
$(L_3 - L_2) = 2 (L_2 - L_1)$
Solution
$L_1 = \frac{\lambda}{4}$, $L_2 = \frac{3\lambda}{4}$ and $L_3 = \frac{5\lambda}{4}$ $\left(\because L = (2n - 1)\frac{\lambda}{4}\right)$