Example 3.5. Let us discuss a sinusoidal wave moving in the +x direction.
y1(x,t)=AsinT2π(t−vx)
A wall located at x=L reflects this wave. Answer the following questions for each of the following two cases: (a) The wall is a fixed end. (b) The wall is a free end.
(1) Find the expression for the reflected wave.
(2) Find the expression for the resultant wave produced by the incident wave and the reflected wave.
Note that a fixed end is an end where the amplitude of the resultant wave of the incident and reflected waves vanishes at all times, whereas a free end is an end where the displacement of the reflected wave is equal to that of the incident wave.