How Do You Solve the Wave Equation on a Half-Line?

[sarahisme]

lol my head is about to explode! :P

i think this is similar to a previous question i asked but i can't quite get it none the less...

http://img137.imageshack.us/img137/7796/picture11gf9.png

now what i did was to following this :

http://img100.imageshack.us/img100/951/picture12yv1.png

then using equations (31) & (32) from that i just plugged in the values and got:

u(x,t) = 1 for x > ct and u(x,t) = 0 for 0 < x < ct

how does this look to you intelligent mathematically inclined people? :S

Sarah :)

 

[sarahisme]

but then how do you find a singularity when you have an answer of 1 and 0? :S