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.
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.