Problem 3
Two point sources S₁ and S₂ oscillate coherently in phase at frequency f in a uniform medium where waves travel at speed c, so λ=c/f. At point P their distances are r₁ and r₂. Assume equal amplitudes, no absorption, and phase difference due only to path difference. (a) Find the phase difference at P in terms of Δr=r₂−r₁. (b) State constructive and destructive conditions. (c) As P moves so Δr increases continuously from 0 to 3λ/2, count maxima and minima crossed, including endpoints when applicable. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
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Collect results in the order asked. Dimensions and physical signs provide independent checks; they do not replace the derivation but can expose algebraic errors.