Question

Question 2 Find the solution 11(x, 1) for the 1-D wave equation aT = (a) 25-for -o <x < oo with initial conditions it (x,0) = A (x) , where A(x) is 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 1, somewhat similar to fex) on page 8s of the Notes Part 2. 2 d2+5 r-0 di+10 di+15 di+20 3 (b) Check for the wave equation in (a) that if f(rtct) (use appropriate value of c) is the solution then g (x, t)-/(x ± ct)-/(-x ± ct) is also a solution. Show that g (0, t) = 0 . Now use (a) and (b) to find the solution u(x,t) for the 1-D wave equation (c) for 0 x < oo with the initial conditions as in (a) (but for 0 x < 00 ) and the boundary condition u(0,1)- 0. This problem describes the motion of the infinitely long elastic string fixed at a wall at one end. (d) Draw the solution to (c) on two separate graphs for t = 2(d, + 1 5) / 5 and t = (d, + 1 5) / 5 carefully noting position and height of the wave shape . d1.3,d2:
d1= 3 & d2= 2

Answer 1

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