3. Interference with Phase Shift Consider two waves y1 and y2 traveling in opposite directions: V1 = A cos(kx - wt) 12 = A cos ( kx + wt + ) where k = 2n/A and w = 2nf = 2n/T. Each wave has the same frequency and amplitude but are separated by a phase shift p. (a) What is the resulting interference pattern y = V1 + 12? Simplify your answer for this standing wave as a product of terms rather than a sum. Write your answer in terms of the given variables, and simplify as much as possible. (b) What are the positions of all the nodes? Write your answer in terms of the given variables. If you create a variable when making a list, you must define it. Note: For parts (b) and (c), write your answer in terms of 2, not k. (c) Find the separation Ax = X2 - X1 between the first node and the second node. sentence. (d) How does the node spacing Ax depend on the phase shift ? State your answer in one