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.
Dec 14th 2009, 04:57 PM
I would first define the odd-extension into the interval which below I'm using Piecewise in Mathematica:
I don't have mathematica, and I think I am supposed to use an even extension on this problem, but I still have another question that I guess I still don't understand. In the equation 1/2[f(x-t) + f(x+t)], how exactly is it used?
For example, how do I know which x coordinates to use?
or which values for time (t) to pick?
I know I am making it more complicated than it is, but I just don't get this part yet.