Struck String

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.

Figure 3: Evenly-struck vibrating string with rigid terminations

For convenience, we are using the velocity $v(t,x)$ 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 [1].