First slide

Stationary waves

Question

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

Moderate

A

1 : 2
B

1 : 3
C

3 : 8
D

3 : 4

Solution

First overtone of closed organ pipe $n_{1} = \frac{3 v}{4 l_{1}}$
Third overtone of open organ pipe $n_{2} = \frac{4 v}{2 L_{2}}$
$n_{1} = n_{2}$ (Given) $\Rightarrow \frac{3 v}{4 L_{1}} = \frac{4 v}{2 L_{2}} \Rightarrow \frac{L_{1}}{L_{2}} = \frac{3}{8}$

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