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Standard XII

Physics

Standing Waves in Closed Organ Pipe

An organ pipe...

Question

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

3/8

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Solution

The correct option is B 3/8
First overtone of closed organ pipe:
$\frac{3 λ}{4} = L_{1}$

$f_{1} = \frac{v}{λ_{1}} = \frac{3 v}{4 L_{1}}$

Third overtone of open organ pipe:

$\frac{4 λ}{2} = L_{2}$

$f_{2} = \frac{v}{λ_{2}} = \frac{2 v}{L_{2}}$

Given $f_{1} = f_{2}$

$\frac{3 v}{4 L_{1}}$ $= \frac{2 v}{L_{2}}$

$\Rightarrow \frac{L_{1}}{L_{2}} = \frac{3}{8}$

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