A2 Daily A Level Physics question
In a resonance-tube lab, a vertical glass tube has its lower end under water (so the air column is closed at the bottom) and the top end open. A single tuning fork of fixed frequency is held at the top while the water level is slowly lowered, producing three successive loud resonances at air-column lengths L1, L2 and L3 (measured from the water surface to the mouth). Which relationship between these lengths must be true for this open–closed air column?
Answer
The correct answer is A.
Correct: A — The increase from L1 to L2 is the same as from L2 to L3; successive resonant lengths are equally spaced for this open–closed air column. A closed end is a displacement node and the open end an antinode, so allowed lengths are odd multiples of a quarter-wavelength; each successive resonance adds half a wavelength to the air column, giving equal spacing. B is wrong because in a closed tube the second resonance corresponds to three-quarters of a wavelength, so L2 is about three times L1, not twice. C is wrong because modes do not add in length this way; the third resonance is at five-quarters of a wavelength, whereas L1 + L2 equals one full wavelength. D is wrong because the fixed step is half a wavelength, not L1 (which is a quarter-wavelength), so taking steps of size L1 would incorrectly predict L2 = 2L1.