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An organ pipe $P_{1}$ closed at one end vibrating in its first harmonic and another pipe $P_{2}$ open at both ends vibrating in its third harmonic are in resonance with a given tuning fork. The ratio of the length of $P_{1}$ to that of $P_{2}$ is:

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8/3

3/8

1/6

1/3

answer is C.

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Detailed Solution

close end tube $P_{1}$ first harmonic is $\frac{v}{4 l_{1}}$ and for $P_{2}$ third harmonic is $\frac{3 v}{2 l_{2}}$ given $\frac{v}{4 l_{1}} = \frac{3 v}{2 l_{2}}$ $\frac{l_{1}}{l_{2}} = \frac{1}{6}$

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