interpreting wave equation using mathematica

hi can someone please help me solving this problem:
Let u(x, t) be a solution of a wave equation utt − uxx = 0, x ∈ (0, 2π), t > 0 satisfying Neumann boundary conditions ux(0, t) = ux(2π, t) = 0, t > 0 and initial conditions u(x, 0) = g(x), ut(x, 0) = h(x). Choose function g(x) and analyze series solution of this problem using Mathematica program. thank you in advance .

So, you have used Mathematica and got the series solution. What did you get? What are your thoughts?

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