Other initial conditions arise in different situations. For instance, in a piano, a hammer strikes a string to set it into motion. When the hammer strikes the string evenly across the surface of the hammer, a situation similar to the animation in Figure 3 arises. Note how the two pulses reflecting back and forth in the bottom frame interfere with each other when they overlap in space.
For convenience, we are using the velocity as the wave variable here instead of displacement. This is because it is easier to relate the velocity initial conditions to a blow from a hammer. Like displacement waves, velocity waves change sign at rigid string terminations, but this is not true for all possible choices of wave variables .