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Math Help - wave equation - method of reflection

  1. #1
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    wave equation - method of reflection

    Hey, I'm a bit confused on how to implement the method of reflection (is that the correct term?) on the wave equation.
    The exercise is in the attached file.

    My attempt:
    I've extended f(x) to the whole line using even continuation. I guess I'm supposed to do the same thing for g(x).. so I did.
    I know how to write the first term of u(x,y), but I'm having trouble with the second term. How is this integral can be simplified?

    Also, when I did the continuation for f(x) I've drawn arrows (red) for each segment. the arrows represent the so called "direction" of the function (from 0 to 1). Is that always the case?

    Thank you in advance






    *sorry for the spelling mistakes
    Attached Thumbnails Attached Thumbnails wave equation - method of reflection-continouation.jpg   wave equation - method of reflection-continouatoin2.jpg  
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