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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 is vibrating in its first overtone and another organ pipe $P_{2}$ opened at both ends is vibrating in its third overtone are in resonance with a given tuning fork. The ratio of length of organ pipe $P_{1}$ and $P_{2}$ is

\frac{1}{3}

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\frac{3}{8}

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\frac{2}{3}

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\frac{8}{3}

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Solution

The correct option is B $\frac{3}{8}$
Both pipes are in resonance with a given tuning fork, therefore, both pipes will have the same frequency of vibrations.
For organ pipe closed at one end,
First overtone $(n = 3)$ ,
$f = \frac{3 v}{4 l_{1}}$ ..........(1)
For organ pipe open at both ends,
Third overtone $(n = 4)$ ,
$f = \frac{4 v}{2 l_{2}}$ ..........(2)
From (1) and (2),
$\frac{3 v}{4 l_{1}} = \frac{4 v}{2 l_{2}}$
$\Rightarrow \frac{l_{1}}{l_{2}} = \frac{3}{8}$

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Standing Waves in Closed Organ Pipe

Standard XII Physics

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

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