how to get one continuous line?

I am trying to get a simple line to 'wave' across the stage and repeat itself. when I loop it, i still get the ten frames or so of the wave entering the stage. although I do want the wave to enter the stage in the beginning, I only need it to do it once. I solved part of this problem with AS, but I can't seem to get the waves to match up end to end because I keep getting a 'jog' in what is supposed to be an otherwise smooth wave. I know it's simple, I just can't get there from here! any ideas would be helpful.
:confused:

have you got an online example we can see?

here is a paired down version so you get the general idea. Thanks.