AS Daily A Level Physics question
In a lab, a 0.75 m air column is closed at one end and driven by a loudspeaker at the open end. Strong resonances are observed at 230 Hz and then at 690 Hz. The cork is removed so the tube is now open at both ends; the length and room conditions are unchanged. Which frequency is now the lowest resonance for this open tube?
Answer
The correct answer is D.
Correct: D — 460 Hz. In a closed–open tube the resonances are odd multiples, so 230 Hz and 690 Hz show f3 = 3f1 and hence f1 = 230 Hz; opening both ends changes the boundary conditions so the fundamental doubles for the same length, giving 2 × 230 Hz = 460 Hz. A 230 Hz — ignores the change from one closed end to two open ends, which raises the fundamental by a factor of 2. B 345 Hz — this is 690/2, a mistaken halving of the higher resonance, not the correct doubling of the closed-tube fundamental. C 690 Hz — confuses a higher closed-tube resonance with the new fundamental of the open tube; the lowest resonance must be below this. D 460 Hz — correct because an open–open tube has a fundamental at twice the closed–open tube’s fundamental for the same length.