wave Consider a 2m long medium in which a wave might propagate. The ends of the medium restrict the wa so that the wave always has an amplitude of 0 at those endpoints. Initially, there is no wave, but the medium is disturbed so that the rate of change of the wave over time is initially given by the function which, when plotted, looks like: 0.5 f(x) = {2 if 0 < x < 1 x if 1x2 0 0 0.5 1 1.5 2 In this scenario: Let u(x, t) be the function describing the amplitude of the wave over time. The medium has a speed of propagation of c = 1/10. You can suppose that t = 0 corresponds to the instant the medium is disturbed (so u(x, 0) = f(x)). (a) (3 Points) Calculate a Fourier sine series for f(x) on the interval 0 < x