An organ pipe $P_1$ closed at one end vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in a resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is :
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Length of pipe closed at one end for first overtone, $l_{1}=3 \pi / 4$
Length of pipe closed at both ends for third overtone; $l_{2}=3 \pi / 4$
$\pi=$ wavelength
$l_{2}=\frac{4 \pi}{2}=2 \pi$
$\therefore \frac{l_{1}}{l_{2}}=\frac{\frac{3 \pi}{4}}{2 \pi}=\frac{3 \pi}{4 \times 2 \pi}=\frac{3}{8}$
$l_{1}: l_{2}=3: 8$
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