AS Daily A Level Physics question
In a lab, two air columns each of length L are set up: Tube A is open at both ends, and Tube B is closed at one end. Tube B is adjusted to its next resonance above its fundamental (second resonance). Which harmonic of Tube A would have the same frequency as Tube B at this setting? Assume the speed of sound is the same in both tubes and ignore end corrections.
Answer
The correct answer is D.
Correct: D — No harmonic of the open tube matches. For the closed tube at its second resonance the frequency is 3v/(4L); for the open tube the nth harmonic is n v/(2L). Equating gives n v/(2L) = 3v/(4L) so n = 3/2 = 1.5, not an integer, so no open-tube harmonic matches. A is wrong because the open-tube fundamental f = v/(2L) is lower; the closed-tube second resonance is 1.5 times this, not equal. B is wrong because the closed tube does not have even harmonics; its second resonance is the third pattern, not matching n = 2 for the open tube. C is wrong because the open-tube third harmonic is 3v/(2L), which is twice 3v/(4L), so it is too high in frequency. D is correct as shown by the ratio n = 3/2.