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

First overtone of closed (P1) = Third overtone of open (P2)∴ 3v4l1=4v2l2⇒l1l2=38

First overtone of closed (P1) = Third overtone of open (P2)∴ 3v4l1=4v2l2⇒l1l2=38

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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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$\frac{2}{3}$

$\frac{3}{8}$

$\frac{8}{3}$

$\frac{1}{3}$

answer is D.

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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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