4. Consider two point sources S and S2 in the adjacent figure, which emit spherical waves of the same frequency f and amplitude A. The waves start in the same phase, and this phase relation at the sources in maintained throughout time. Consider point P at which ri is nearly equal to 12. (a) Show that the superposition of these two waves gives a wave whose amplitude varies with the position P approximately according to Ym 2A k cos (11-12) in which r=(1+72)/2. (b) Then show that total cancellation occurs when r-r2 = (n+1)A, n being any integer, and that total reinforcement occurs when r = n. (Hint: you will need to make some approximations about how the amplitude of the waves decays with distance. The interference effects you are calculating depend mainly on the phase of the interfering waves.) $2 12