Two sources have a phase difference 0 that is proportional to time: 0 = Ct, where C

Question:

Two sources have a phase difference δ0 that is proportional to time: δ0 = Ct, where C is a constant. The amplitude of the wave from each source at some point P is A0.

(a) Write the wave functions for each of the two waves at point P, assuming this point to be a distance x1 from one source and x1 + ∆x from the other.

(b) Find the resultant wave function, and show that its amplitude is 2A0 cos ½ (δ + δ0), where δ0 is the phase difference at P due to the path difference.

(c) Sketch the intensity at point P versus time for a zero path difference. (Let I0 be the intensity due to each wave separately.) What is the time average of the intensity?

(d) Make the same sketch for the intensity at a point for which the path difference is ½ λ.