A2 Daily A Level Physics question

2026-06-02 OCR A Waves I: progressive waves; c = fλ; superposition; phase; intensity ∝ amplitude² (qual.) OCR-A Module 4.1.1 Progressive waves and phase OCR-A Module 4.3.1 Principle of superposition of waves OCR-A Module 4: Intensity proportional to amplitude squared (qualitative)

Two identical loudspeakers are driven by the same signal (so they are coherent and in phase). At a microphone P, the path difference from the two speakers is exactly one-third of the wavelength of the tone. Which statement about the sound intensity at P must be true, compared with using only one speaker?

A It is the same as with one speaker alone, because the resultant amplitude equals that from a single source for a 120° phase difference. (correct)
B It is about twice that with one speaker, because the equal intensities simply add.
C It is four times that with one speaker, because the amplitudes add to double.
D It is about half that with one speaker, because partial cancellation significantly reduces the amplitude.

Answer

The correct answer is A.

Correct: A — It is the same as with one speaker alone, because the resultant amplitude equals that from a single source for a 120° phase difference. For a path difference of λ/3, the phase difference is 120°, giving resultant amplitude 2A cos(60°) = A, so intensity (∝ A²) is unchanged relative to one source. B is wrong because adding equal intensities (2I) ignores coherence and phase; with 120° phase difference the vector sum of amplitudes does not give 2I. C is wrong because doubling amplitude (and hence quadrupling intensity) only occurs for 0° phase difference (in phase at P), not at 120°. D is wrong because a 120° phase difference does not reduce the amplitude to 1/√2 of A (which would give half intensity); here the resultant amplitude equals A so the intensity stays the same.

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