A2 Daily A Level Physics question
In a quiet lab, two identical speakers emit the same 1.0 kHz tone in phase and at equal amplitude. A microphone is placed exactly midway between them. With only one speaker on, the microphone reads an average sound intensity I. Both speakers are then turned on at the same settings. Neglect reflections. What intensity is now measured at the microphone?
Answer
The correct answer is D.
Correct: D — becomes 4I. At the midpoint the waves arrive in phase with equal amplitude, so the resultant displacement amplitude doubles and intensity, being proportional to amplitude squared, becomes 4I. A — stays at I is wrong because adding a second coherent in-phase source increases the amplitude, not leaving intensity unchanged. B — becomes 2I is wrong because that adds intensities directly; in-phase coherent addition doubles amplitude, giving four times the intensity. C — drops to nearly 0 is wrong because cancellation would require a 180° phase difference or a half-wavelength path difference, which is not the case at the midpoint with in-phase sources. D — becomes 4I is correct because amplitude doubles and intensity scales with the square of amplitude.