Question

Question 2 ul lu (a) Find the solution u(x,t) for the 1-D wave equationfor -oo < x < oo with initial conditions u (x,0)-A(x) , where A(x) s presented in the diagram below, and zero initial velocity. For full marks u(x,t) needs to be expressed as an equation involving x and t, somewhat similar to f(x) on page 85 of the Notes Part 2. di+10 dı+15di+20 (b) Check for the wave equation in (a) that if f(xtct) (use appropriate value of c) is the solution then g(x, Đ = f(x ± ct)-f(-x ± ct) is also a solution. Show that g(0,1)-0 (c)Now use (a) and (b) to find the solution u(x,t) for the 1-D wave equation for O 3x<oo with the initial conditions as in (a) (but for 0 3x<) and the boundary condition u(0,t)-0. This problem describes the motion of the infinitely long elastic string fixed at a wall at one end. Draw the solution to (c) on two separate graphs for t 2(d +15)/5 and t- (d, +15)/5 carefully noting position and height of the wave shape

Answer 1

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