Waves "flip" (or invert) primarily due to a change in medium, specifically when a wave encounters a boundary transitioning to a medium with a lower wave speed. This is most noticeable with reflected waves.
Here's a breakdown:
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Reflection at a Boundary: When a wave traveling in one medium (like a rope) encounters a boundary with another medium where the wave travels slower, part of the wave is reflected back.
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Fixed-End Analogy: The boundary, when reflecting the wave back into the original medium, behaves like a "fixed end." Imagine tying a rope to a wall. When you send a wave down the rope, the point where the rope is tied to the wall can't move up or down freely.
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Inversion: Because the end is "fixed," the wave exerts a force on it. By Newton's Third Law (for every action, there is an equal and opposite reaction), the wall exerts an equal and opposite force back on the rope. This reaction force causes the reflected wave to be inverted. The crest becomes a trough, and vice-versa.
Example:
Imagine shaking a rope tied to a wall. The wave you send down the rope will hit the wall and bounce back. The returning wave will be flipped – a crest will become a trough, and vice versa. This is because the wall acts as a "fixed end," forcing the inversion.
In Summary: Waves flip (invert) upon reflection when they encounter a boundary leading to a slower-velocity medium because the boundary acts like a fixed end, resulting in an equal and opposite reaction that inverts the reflected wave.
