Problem 1: 1D wave equation (Submit) Consider an infinite string subject to the initial conditions a(z,0) = f(z) = 1-r if 0 z 0 m(z, 0) = g(x)-0. Assume that for this string (T/P) 1/2-1, with T being the tension in the string and ? the density of the string per its unit length. (a) In the x-t plane draw the important characteristics that can be interpreted from the D'Alembert's solution. Using these characteristics identify different regions in the x-t plane that have the same expression for the displacement of the string. Find the expression for the displacement in each region. Then, use this geometric interpretation of the D'Alembert's solution to sketch the shape of the string at times t 0, 1/2, 1 and 2. (b) Use the Matlab code attached to this assignment to solve this problem numerically. Attach the plots for the shape of the string at any time to your assignment. Note that the small-scale oscillations in these plots are numerical artifacts and not physical. Com- pare the location of the peaks of the waves at each time from the numerical solution and D'Alembert's solution