I have the following question on this problem:
Utt = Uxx, 0<x<infinity, 0<t
Ux(0,t) = 0
U(x,0) = f(x)
Ut(x,0) = 0
f(x) is given as a graph: a triangle with left bottom corner at x = 2
right bottom corner at x = 4
height of the triangle at y = 2.
I am asked to give a detailed picture for different time values to show the periods: 1) during separation of the wave into 2 smaller waves
2.) before bounding from x = 0, 3.) during bouncing from x = 0
and 4.) long time after bouncing from x= 0.
I know I have to use the D'Alembert's Eqn: U(x,t) = [f(x-ct) + f(x+ct)]/2, but I don't have any clue as to how to get the times, or how to obtain the picture at that time. Can anybody get me started/show me an example as I am seriously confused on this. Thanks.