Physics
Physics
Problem
A pulse of amplitude travels along a string and reaches an end that is free to move. (i) What is the amplitude of the reflected pulse? (ii) What is the maximum instantaneous displacement of the end just after reflection?Intuitive explanation
When a wave pulse hits a free end, the boundary condition is that there's no force constraint—the end can move freely. This means the reflected pulse inverts its direction of travel but preserves its amplitude, unlike a fixed end which would invert the pulse shape itself. The key insight is that at a free end, the incident and reflected pulses add together in the region near the boundary, creating constructive interference that can temporarily double the displacement.
Intuitive explanation
When a wave pulse hits a free end, the boundary condition is that there's no force constraint—the end can move freely. This means the reflected pulse inverts its direction of travel but preserves its amplitude, unlike a fixed end which would invert the pulse shape itself. The key insight is that at a free end, the incident and reflected pulses add together in the region near the boundary, creating constructive interference that can temporarily double the displacement.