A2 Daily A Level Physics question
In a resonance-tube experiment, a student holds a 300 Hz tuning fork above a vertical tube that is open at the top and closed at the bottom. The first loud resonance occurs when the air column length is 28 cm (ignore end corrections). The student then opens the bottom so the tube is open at both ends and uses the same tuning fork. What is the shortest tube length that will now produce a strong resonance?
Answer
The correct answer is C.
Correct: C — 56 cm. With one end closed, the first resonance fits a quarter of a wavelength, so the wavelength is 4 × 0.28 m = 1.12 m; with both ends open, the shortest resonant length is half a wavelength, so L = 1.12/2 = 0.56 m (56 cm). A 14 cm would be one-eighth of a wavelength, which does not satisfy the open–open condition. B 28 cm leaves a quarter-wavelength pattern, incompatible with antinodes at both ends. C is correct because open–open columns resonate at multiples of half-wavelength, and the smallest is λ/2 = 56 cm. D 84 cm corresponds to 3λ/4 for a closed tube (a common mix-up) and is not a valid multiple of λ/2 for an open–open tube.