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Atmospheric Pressure

Two closed pi...

Question

Two closed pipes have the same fundamental frequency. One is filled with oxygen and the other with hydrogen at the same temperature. Ratio of their lengths respectively is:

A

1 : 4

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B

4 : 1

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C

1 : 2

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D

2 : 1

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Solution

The correct option is A $1 : 4$

We know that for closed pipes: $n = \frac{V}{4 l}$

As they have same fundamental frequency: $\frac{V_{H}}{V_{0}} = \frac{l_{H}}{l_{0}}$

Since velocity of a gas is inversely proportional to it's molecular mass:
$\frac{V_{H}}{V_{0}} = \sqrt{\frac{M_{2}}{M_{1}}} = \sqrt{\frac{32}{2}} = 4$

$V_{0} : V_{H} = 1 : 4$
$\Rightarrow l_{O} : l_{H} = 1 : 4$

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