Wave Reflection & Refraction at Boundaries Simulator

This simulator sends a single pulse traveling down a string toward a boundary and lets you choose what that boundary is: a fixed end (like a rope tied to a wall), a free end (like a ring sliding on a frictionless pole), or a change into a second medium with a different wave speed. Each boundary produces a distinctly different reflected — and, for the medium-change case, transmitted — pulse.

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About the Wave Reflection & Refraction at Boundaries Simulator

This simulator sends a single pulse traveling down a string toward a boundary and lets you choose what that boundary is: a fixed end (like a rope tied to a wall), a free end (like a ring sliding on a frictionless pole), or a change into a second medium with a different wave speed. Each boundary produces a distinctly different reflected — and, for the medium-change case, transmitted — pulse.

What the simulator shows

• A traveling pulse launched repeatedly down a string toward a selectable boundary type. • Fixed-end and free-end presets showing the reflected pulse returning inverted or upright, respectively. • A medium-change preset showing the pulse partially reflect and partially transmit at the boundary, with the transmitted pulse changing speed and width in the new medium. • Live readouts describing the reflection type and whether the reflected pulse undergoes a phase inversion.

Why the boundary condition controls the reflection

At a fixed end, the string itself cannot move, which forces the reflected pulse to arrive upside-down (inverted) relative to the incoming pulse — the only way the sum of incoming and reflected displacement can equal zero at that point. At a free end, the string tip is free to swing to its maximum displacement, and the reflected pulse comes back right-side up (no inversion). At a boundary between two different media, the wave partially reflects and partially transmits; when moving into a slower medium the reflected component inverts (behaving similarly to hitting a fixed end), and when moving into a faster medium it does not invert (behaving similarly to a free end) — with the transmitted pulse always changing speed and wavelength to match the new medium while frequency stays the same.

Frequently asked questions

Why does a pulse invert when it reflects off a fixed end?

At a fixed end, the string cannot move at that point. The only way for the sum of the incoming and reflected wave to stay at zero displacement there is for the reflected pulse to be an inverted (upside-down) mirror image of the incoming pulse.

Why does a pulse NOT invert when it reflects off a free end?

At a free end, the string tip is unconstrained and can swing to its full displacement — nothing forces cancellation there, so the reflected pulse returns right-side up, with the same orientation as the incoming pulse.

What happens when a wave crosses into a medium with a different speed?

Part of the wave reflects at the boundary and part transmits into the new medium. The transmitted portion changes speed (and therefore wavelength, since frequency stays constant) to match the new medium; the reflected portion inverts if the new medium is slower, and stays upright if the new medium is faster.

What does this simulator leave out?

It shows an idealized single pulse with clean single reflections and no multiple internal reflections, energy loss at the boundary, or the continuous-wave standing-wave patterns that arise when a periodic driving source (rather than a single pulse) is used against these same boundaries.

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