Wave Pulse Reflected at Fixed End of String

The toggle button on the right reveals a matching pulse moving along an identical but longer string meeting a negative pulse exactly in the middle, corresponding to the fixed end of the string above.  Since the two pulses in the longer string are equal and opposite in amplitude, they cancel at the midpoint, which never moves: so the left-hand half of the longer string has the same boundary conditions and initial configuration as the fixed-end string, and will move in exactly the same way.