Problem 3
Two coherent point sources S₁,S₂ emit sinusoidal waves in phase, each of amplitude A and wavelength λ in a uniform medium. At point P let path difference be Δr=r₂−r₁; take source phase as zero and ignore amplitude decrease with distance. (a) Express the phase difference between waves arriving at P. (b) Find Δr values for intensity maxima and minima. (c) Write resultant intensity in terms of the one-source intensity I₁ and give its maximum and minimum. 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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problems.proof.analysis
Collect results in the order asked. Dimensions and physical signs provide independent checks; they do not replace the derivation but can expose algebraic errors.