let

y(x, t) := f(x − ct) − f(−x − ct).

Show that y is a solution of the wave equation c2yxx = ytt and that

y(0, t) = 0 for all t. Describe what is happening here in terms of

incident and reflected waves.

(ii) If, by contrast,

y(x, t) := f(x − ct) + f(−x − ct)

show that y is once again a solution of the wave equation. What

boundary condition does y now satisfy at x = 0? Describe what

is happening here in terms of incident and reflected waves.

I can do it all except for the explanation bit.. I'm guessing that in the first one, the reflected wave is coming back along the line of the incident wave, and in the second one, its waves are reversed.. but this is really a guess

any help much appreciated