Help with quantum mechanics homework problem

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Homework Statement

see attached :)

Homework Equations

The Attempt at a Solution

Not sure how to start..! Any hints? Thanks!

 

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anyone..?

 

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Ok I've done all of this question now apart from the bit where it asks us to determine the phase difference of the beams at the detector. How do i do this bit?

I know that the phase of the first wave is (kx - kvt) and the phase of the second is (k'x - k'v't)