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. Pipe B is open at one end and closed at the other end, and is filled with a diatomic gas of molar mass MB . 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. 

(b) Now the open end of pipe B is closed (so that the pipe is closed at both ends). Find the ratio of the fundamental frequency of pipe A to that in pipe B.

Answer 1

(a) The frequency of second harmonic of pipe A

(b) When pipe B is closed at both ends, its frequency

Answer 2

(b) Fundamental frequency in pipe A = v_A/2l

Fundamental frequency in pipe B = v_B/2l

The ratio of the fundamental frequencies = v_A/v_B = 3/4.