Two narrow cylindrical pipes A and B have the same length. Pipe A is open at both ends and is filled with a monoatomic gas of molar mass $M_{A}$ . Pipe B is open at one end and closed at the other end, and is filled with a diatomic gas of molar mass $M_{B}$ . Both gases are at the same temperature. (a) If the frequency of the second harmonic of the fundamental mode in pipe A is equal to the frequency of the third harmonic of the fundamental mode in pipe B, determine the value of $\frac{M_{A}}{M_{B}}$ . (b) Now the open end of pipe B is also closed (so that the pipe is closed at both ends). Find the ratio of the fundamental frequency in pipe A to that in pipe B. Choose the option containing the correct final result.
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Question

Two narrow cylindrical pipes A and B have the same length. Pipe A is open at both ends and is filled with a monoatomic gas of molar mass M A M_{A} M A . Pipe B is open at one end and closed at the other end, and is filled with a diatomic gas of molar mass M B M_{B} M B . Both gases are at the same temperature. (a) If the frequency of the second harmonic of the fundamental mode in pipe A is equal to the frequency of the third harmonic of the fundamental mode in pipe B, determine the value of M A M B \frac{M_{A}}{M_{B}} M B M A . (b) Now the open end of pipe B is also closed (so that the pipe is closed at both ends). Find the ratio of the fundamental frequency in pipe A to that in pipe B. Choose the option containing the correct final result.

Physics · Wave Motion

G1 Physics · Accepted Answer

Step 1: Identify the governing wave relation from the data and preserve the stated boundary/phase conditions. Step 2: Substitute the numerical values with SI units and simplify. Step 3: Compare with the keyed result from the source. Final: B: (a) 2.116; (b) 3 4 \frac{3}{4} 4 3 ​ .