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A2 Daily A Level Physics question

2026-04-06 OCR A Waves II: stationary waves; harmonics; boundary conditions; string/air column examples OCR-A Module 4.4 Waves: stationary waves in strings and air columns OCR-A Module 4.4: boundary conditions at open and closed ends; harmonics in pipes

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?

  1. 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. (correct)
  2. B L2 is twice L1; the second resonance needs double the air-column length of the first.
  3. C L3 equals L1 plus L2; the third resonance occurs when the first two patterns add together.
  4. D Each step in resonant length equals L1, so L2 would be 2L1 and L3 would be 3L1.

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.