Two narrow cylindrical pipes A and B have the same length. Pipe A is open at both ends and is filled with a monatomic 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 M A /M B . (b) Now the open end 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.

Two narrow cylindrical pipes A and B have the same length. Pipe A is open at both ends and is filled with a monatomic 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 M_A/M_B.

(b) Now the open end 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.