consider the wave equation utt - uxx 0, Mathematics

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consider the wave equation utt - uxx 0

Consider the wave equation u_tt - u_xx = 0 with
u(x, 0) = f(x) = 1 if -1
Please provide me a detailed answer. I had worked the most part of this question and the only I would like to do is to get a comprehensive response to check whether I am 100% right. Thank you!

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