What is the phase accumulation of reflected wave?

[sapz]

Homework Statement

(See picture)
We have 3 areas in which a wave can move.

The wave Y1 starts at area 1 and goes towards Border 1, some part of it is passed to Area 2.
That part goes towards Border 2, and some part of it is reflected back into Area 2.
That part moves towards Border 1, and some of it passes to Area 1.

I'm interested in that last part that returned to Area 1, which is Y4.
What is its Phase? It would seem that the wave accumulated phase when it was in Area 2, so should it be 2D * k2? (wave number times the distance in that area)?

If the original wave was Y_1(x,t) = Ae^{i(wt-k_1x)}, would Y4 be Y_4(x,t) = Be^{i(wt+k_1x+\phi)}, where \phi = 2Dk_2?
Or should it be \phi = -2Dk_2?

(A and B are some amplitudes we can relate through reflectivity and transmittance coefficients)

 

[scottdave]

I think the wave is going to reverse phase at the boundary 2. This site talks about acoustic waves, but I think some of the theory may apply. http://www.acs.psu.edu/drussell/Demos/reflect/reflect.html