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.
problems.proof.stepOf
problems.proof.prevStepproblems.proof.nextStep
Δr signed; phase modulo 2π\Delta r\text{ signed; phase modulo }2\pi
problems.proof.analysis

The phase difference is wave number 2π/λ2\pi/\lambda times signed path difference Δr\Delta r. Keeping its sign records path ordering, while intensity is unchanged by reversing it.

problems.proof.pitfall. Pitfall: using the signed path difference while restricting the order incorrectly. Distinguish the sign of Δr\Delta r from its magnitude ∣Δr∣|\Delta r| when naming fringe orders.