AS Daily A Level Physics question
In a lab, a 0.80 m tube is closed at one end and open at the other. A loudspeaker and signal generator produce strong resonances at 300 Hz and 900 Hz. The tube is then opened at both ends, with its length and the air temperature unchanged. Ignore any end corrections. Which value is now the lowest resonant frequency?
Answer
The correct answer is A.
Correct: A — 600 Hz. In the closed–open tube the first two resonances at 300 Hz and 900 Hz show the odd-harmonic pattern, so the fundamental is 300 Hz; opening both ends changes the pattern so the lowest mode fits half a wavelength in the tube, doubling the fundamental to 2 × 300 = 600 Hz. A is correct because opening the second end changes the node–antinode conditions so the fundamental frequency doubles for the same length. B is wrong because keeping length the same does not keep frequency the same when boundary conditions change. C is wrong because taking the midpoint between 300 Hz and 900 Hz has no physical basis in the allowed standing-wave patterns. D is wrong because 900 Hz was the next allowed resonance for the closed–open case and does not become the new fundamental when both ends are open.