Question

A certain organ pipe filled with oxygen resonates in its fundamental mode at a frequency of 600Hz. The new fundamental frequency if oxygen is replaced by hydrogen at same temperature is?
(A) 2400 Hz
(B) 9600 Hz
(C) 600 Hz
(D) 150 Hz

Answer 1

Hint:We know that there can be two cases when the pipe is open at both the ends or the pipe is closed at one of the ends. When both the ends of the pipe are open then the instrument is said to be an open-end air column. Also, the formula for finding the fundamental frequency when the organ pipe is filled with some gas is given by the formula $v=\sqrt{\dfrac{RT}{M}}$where M is the molar mass of the gas.

Complete step by step answer:
Now when the pipe was filled with oxygen, the fundamental frequency was 600 Hz. Now it is replaced with hydrogen, we know the molar mass for hydrogen gas is 2g and for oxygen gas it is 32g.
Thus,
$\dfrac{{{v}_{O}}}{{{v}_{H}}}=\dfrac{\sqrt{\dfrac{RT}{{{M}_{0}}}}}{\sqrt{\dfrac{RT}{{{M}_{H}}}}}$
$\Rightarrow \dfrac{{{v}_{O}}}{{{v}_{H}}}=\sqrt{\dfrac{{{M}_{H}}}{{{M}_{0}}}}$
$\Rightarrow \dfrac{600}{{{v}_{H}}}=\sqrt{\dfrac{2}{32}}$
$\Rightarrow \dfrac{600}{{{v}_{H}}}=\dfrac{1}{4}$
$\therefore {{v}_{H}}=2400Hz$

So, the correct option is A.

Note:We know that hydrogen does not exist as a single atom but as a diatomic molecule in the form of a gas and the same goes for the oxygen. The molar mass of hydrogen atom is 1g and for hydrogen gas ${{H}_{2}}$there are two hydrogen molecules. Same is the case for hydrogen gas ${{O}_{2}}$where there are two oxygen atoms. Both are diatomic molecules. Also, the fundamental frequency of an organ pipe depends upon the temperature. the positions of the nodes and antinodes of the standing waves is responsible for different sounds produced from the pipes.