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Standing Waves in Open Organ Pipe

The fundament...

Question

The fundamental frequencies of a closed pipe and an open pipe of different lengths are 300 $H z$ and $400 H z$ respectively. If they are joined to Conn a longer pipe, the fundamental frequency of the long pipe so formed is

A

350 H z

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B

50 H z

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C

120 H z

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D

100 H z

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Solution

The correct option is C $120 H z$
We know,

For an open pipe,
$f_{1} = \frac{v}{2 L_{1}} = 400$

For a closed pipe,
$f_{2} = \frac{v}{4 L_{2}} = 300$

When an open and a closed oipe are joined, it forms a longer open pipe,

Length of the longer pipe $= L_{1} + L_{2}$

$f_{0} = \frac{v}{4 (L_{1} + L_{2})}$

$L_{1} = \frac{v}{800}$

$L_{2} = \frac{v}{1200}$

$L_{1} + L_{2} = \frac{5 v}{2400} = \frac{v}{480}$

$f_{0} = \frac{v}{4 (L_{1} + L_{2})} = 120 H z$

Option $C$ is the correct answer

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