When a wave reaches a boundary, the reflected pulse can either flip over or remain upright. That outcome depends on whether the wave speed becomes lower or higher in the next medium.

What wave inversion means

A wave pulse meeting a boundary usually creates a reflected wave that travels back into the original medium. The reflected pulse may keep the same orientation as the incident pulse, or it may reverse across the equilibrium line.

Inversion changes the sign of the displacement, not the direction of travel.

This figure shows a transverse pulse reflecting from a fixed end. The reflected pulse is inverted (a crest returns as a trough), while its direction of travel reverses back toward the source. This is the canonical visual model for “inverted reflection.” Source

The reflected pulse still moves back toward the source; it is just flipped vertically. This is why an upward pulse can return downward after reflection.

For AP Physics 2, the most important question is not the exact shape of the pulse but whether the reflected pulse is inverted or not inverted.

The key rule at a boundary

To determine the reflected pulse behavior, compare the wave speed in the original medium to the wave speed in the medium beyond the boundary.

• If the transmitted wave enters a medium where the wave speed decreases, the reflected wave is inverted.

This notes page compares reflection/transmission for a pulse crossing a boundary into a more dense (slower) medium versus a less dense (faster) medium. The diagrams highlight when the reflected pulse inverts and how speed and wavelength differ across the boundary while frequency remains the same. It’s a quick visual checklist that matches the “slower → fixed-end-like (invert), faster → free-end-like (no invert)” decision rule. Source

• If the transmitted wave enters a medium where the wave speed increases, the reflected wave is not inverted.

This rule is qualitative, but it is very powerful. You do not need a complicated calculation. You only need to decide whether the wave would move slower or faster in the second medium.

A useful way to think about this is that the reflected pulse is responding to how the boundary behaves. A boundary leading to a slower medium resists the motion more strongly. A boundary leading to a faster medium yields more easily.

Why a slower second medium causes inversion

When the second medium supports a lower wave speed, the boundary behaves more like a fixed end. The incident pulse pushes on the boundary, but the boundary does not move as freely as the pulse would prefer. As a result, the disturbance that reflects back is reversed.

This is why a pulse traveling from a medium where waves move relatively quickly into one where they move more slowly reflects inverted. The slower medium acts like a stronger constraint on the motion at the boundary.

In many classroom examples, this happens when a pulse moves from a lighter string into a heavier string, assuming the strings are joined and under similar conditions. The heavier section tends to support a lower wave speed, so the reflected pulse flips.

The important AP idea is the change in speed, not the label “light” or “heavy” by itself. Always base your decision on whether the transmitted wave would be slower or faster.

Why a faster second medium does not cause inversion

When the second medium supports a higher wave speed, the boundary behaves more like a free end. The boundary can respond more easily to the incident pulse, so the reflected disturbance is not reversed.

That means a crest reflects as a crest, and a trough reflects as a trough. The reflected wave still travels back toward the source, but it stays on the same side of the equilibrium line as the incident pulse.

A common example is a pulse moving from a heavier string into a lighter string. Because the second string allows a greater wave speed, the reflected pulse returns upright rather than inverted.

How to interpret pulse diagrams

On diagrams, students often confuse left-right motion with up-down orientation. These are separate ideas.

• The incident pulse travels toward the boundary.

• The reflected pulse always travels away from the boundary and back into the original medium.

• Inversion tells you whether the reflected pulse is flipped vertically.

Use this quick logic:

• Upward pulse into a slower medium $\rightarrow$ reflected pulse is downward.

• Downward pulse into a slower medium $\rightarrow$ reflected pulse is upward.

• Upward pulse into a faster medium $\rightarrow$ reflected pulse stays upward.

• Downward pulse into a faster medium $\rightarrow$ reflected pulse stays downward.

In AP problems, the safest sequence is:

• identify the incident pulse orientation,

• determine whether the next medium has lower or higher wave speed,

• decide whether the reflected pulse inverts.

Common misunderstandings

One common error is to think that inversion depends on the direction the pulse is moving. It does not. Two pulses traveling toward the same boundary can reflect differently only if the medium change is different, not because one came from the left and one from the right.

Another common mistake is to assume that “inverted” means “smaller.” These ideas are different. Inversion describes orientation, while the size of the reflected pulse depends on how the boundary affects the wave.

It is also important not to ignore the second medium. The reflected wave is determined by what happens at the boundary, so the question always asks what kind of medium the transmitted wave would enter.

If the wave speed on the other side is lower, think fixed-end-like behavior and inversion. If the wave speed on the other side is higher, think free-end-like behavior and no inversion.