Physic Labs

Problem 3

Two coherent sources of equal amplitude emit sound in phase of wavelength λ\lambda. At point PP their path difference is Δr\Delta r. Find the conditions for constructive and destructive interference at PP, including the corresponding integer orders. (a) Derive the phase difference at PP from signed path difference Δr\Delta r. (b) Obtain constructive and destructive conditions with integer orders, distinguishing signed difference from its magnitude. (c) Decide whether reversing the path difference or reversing one source’s phase changes the fringe type; check zero and half-wavelength path differences.
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Δr=nλ,n∈Z\Delta r=n\lambda,\quad n\in\mathbb Z
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Equal-amplitude waves add constructively when phase difference is 2πn2\pi n, with integer nn. Substitution gives the maximum condition Δr=nλ\Delta r=n\lambda.