### Wave Reflection Explained...

A pulse traveling down a string and reflected from a fixed end will be reversed (up to down), but reflected from a free end it will stay up.

This can be understood by imagining a string twice as long, of the same thickness and tension, with equal pulses having opposite velocities coming in from the two ends to pass through each other in the middle. As an up pulse passes through a down pulse, the middle of the long string never moves – so the left-hand half of the string, which satisfies the same identical equation of motion as the string with the fixed end, and has the same “boundary condition” of never moving at the center point, behaves in exactly the same way.

By a string having a "free" end, we mean the end is free to move vertically, but the string is still under tension. This is realized by having at the string end a ring of negligible mass moving on a frictionless vertical pole. The string tension can have no vertical component at the end, or the ring would accelerate at an infinite rate, so the string must end horizontally at all times.

Two identical pulses meeting symmetrically on the longer string will add to zero slope at the central point, so one-half of the longer string will behave exactly like the shorter string with free end.

Code by Casey Bowler