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.
problems.proof.stepOf
problems.proof.analysis
The next part uses the preceding result as input rather than treating parts independently. This keeps conventions and physical state consistent throughout.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.