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AS Daily A Level Physics question

2026-03-05 OCR A Waves II: stationary waves; harmonics; boundary conditions; string/air column examples OCR-A Module 4: Waves — Stationary waves; strings and air columns; boundary conditions OCR-A 4.1.4 Stationary waves (harmonics in strings and pipes)

Two organ pipes of equal length L are at the same temperature. Pipe X is open at both ends; pipe Y is closed at one end (stopped). Each is sounded at its fundamental. Assuming the speed of sound is the same in both, what is the ratio of their fundamental frequencies f_X : f_Y?

  1. A 2 : 1 (correct)
  2. B 1 : 2
  3. C 1 : 1
  4. D 4 : 1

Answer

The correct answer is A.

Correct: A — 2 : 1. A For fundamentals: open–open gives L = λ/2 and closed–open gives L = λ/4, so with the same sound speed v, f_X : f_Y = (v/2L) : (v/4L) = 2 : 1. B Inverts the ratio, wrongly giving the closed pipe the higher fundamental even though its fundamental wavelength is longer. C Assumes both have the same fundamental despite different boundary conditions setting different wavelengths. D Overstates the effect by a factor of two; confusing half- vs quarter-wave does not give 4:1.

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