Question

There are two narrow pipes A and B of equal length l. Pipe A is filled with Helium gas and pipe B is filled with a hypothetical diatomic gas whose mass is 7/6 times the molar mass of hydrogen. Both gases are at the same temperature.

Choose the correct statement from the following.

• A. Pipe-A can resonate with pipe-B if both pipe-A and pipe-B are open pipes
• B. Pipe-A can resonatewith pipe-B if pipe-A is closed and pipe-B is open pipe
• C. Pipe-A can resonate with pipe-B if pipe-A is open and pipe-B is closed
• D. Pipe-A can resonate with pipe-B if both pipes are closed-pipes

Answer 1

Answer: (A), (C)

Pipe-A can resonate with pipe-B if both pipe-A and pipe-B are open pipes
Pipe-A can resonate with pipe-B if pipe-A is open and pipe-B is closed

$V_A=\sqrt{\frac{{\gamma }_{A}RT}{M_{HE}}}=\sqrt{\frac{5RT}{12m}}$, and $V_B=\sqrt{\frac{{\gamma }_{B}RT}{M_{H_2}}}=\sqrt{\frac{\left(7/5\right)RT}{2m\times 7/6}}=\sqrt{\frac{3RT}{5m}}$

Case-I: When both pipes are closed at one ends.

$(2n-1)\sqrt{\frac{5}{12}}=(2m-1)\sqrt{\frac{6}{10}}\Rightarrow \frac{2n-1}{2m-1}=\frac{6}{4}$ [Not possible]

Case-II: when both pipes are open at both ends

$\frac{n}{m}=\sqrt{\frac{36}{25}}=\frac{6}{5}\Rightarrow n=6,m=5$.

Case-III: When pipe A is closed at one end and pipe - B is open at both ends.

$\frac{2n-1}{2m}=\sqrt{\frac{36}{25}}=\frac{6}{5}$ [Not possible]

Case-IV: When pipe A is open at both ends and pipe - B is closed at one end.

$\frac{2n}{2m-1}=\frac{6}{5}\Rightarrow n=3,m=2$ [Possible]