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Semi- Infinite String: consider the following wave equation describing the semi-infinite vibrating string problem = x>0, t>0, 612 6x2 ' "(130) = f(x), x > 0 Bu 5(3550) _ 05), x > 0 u ax(0,t)_0, t> 0 a) Find the d'Alembert's solution to the initiaVboundary value problem. [Assuming that u is continuous at x=0, t=0.] b) Show that the solution found in part (a) maybe obtained by extending the initial position and velocity as even functions (around x = 0)