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Q.

An organ pipe P₁ is closed at one end and vibrating in its first overtone and another pipe P₂ opened at both ends vibrating in its third overtone are in resonance with a given tuning fork. Then, the ratio of lengths of P₁ and P₂ is

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a

$\frac{2}{3}$

b

$\frac{3}{8}$

c

$\frac{8}{3}$

d

$\frac{1}{3}$

answer is D.

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Detailed Solution

First overtone of closed (P₁) = Third overtone of open (P₂)

$∴ 3 (\frac{v}{4 l_{1}}) = 4 (\frac{v}{2 l_{2}}) \Rightarrow \frac{l_{1}}{l_{2}} = \frac{3}{8}$

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