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  4. An organ pipe P1 closed at one vibrating in its first overtone and another pipe P2 open at both ends vibrating in third overtone are in resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is

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Q. An organ pipe $P_{1}$ closed at one vibrating in its first overtone and another pipe $P_{2}$ open at both ends vibrating in third overtone 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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Solution:

$3 \times \frac{v}{4 l_{c}}=4 \times \frac{v}{2 l o}$
or $\frac{l_{c}}{l o}=\frac{3 v}{4} \times \frac{2}{4 v}$
$=\frac{3}{8}$