AP Syllabus focus: 'A wave traveling from one medium to another may be transmitted or reflected depending on the boundary. Reflected and transmitted waves can occur together.'
When a wave reaches the edge of one medium or enters a new one, its behavior depends on that transition. The key ideas are reflection, transmission, and recognizing that both often happen together.
Meeting a boundary
A wave travels through a medium until it encounters a change. That change might be a rope tied to a different rope, sound reaching a wall, or light reaching glass. The place where the change occurs is called a boundary.
Boundary: The surface or region where one medium ends and another medium begins.
The wave arriving at the boundary is the incident wave. At that point, the disturbance cannot simply continue unchanged, because the conditions on the other side are different. The boundary responds to the incoming disturbance, and the result is often a split in the wave’s motion.
Part of the incoming disturbance can remain in the original medium and move away from the boundary. That part is the reflected wave.
Reflected wave: The part of an incident wave that returns into the original medium after reaching a boundary.
At many real boundaries, the incoming wave is not sent completely backward. Another part can continue beyond the boundary and enter the new medium. That part is the transmitted wave.
Transmitted wave: The part of an incident wave that enters the second medium after reaching a boundary.
These two outcomes are not mutually exclusive.
Diagram of a pulse reaching a boundary between two ropes, showing the incident pulse splitting into a reflected pulse in the original medium and a transmitted pulse in the second medium. This visualization reinforces that reflection and transmission can occur simultaneously at a single interface. Source
A single incident wave can produce a reflected wave and a transmitted wave at the same time.
Why boundaries produce different outcomes
The specification emphasizes that what happens depends on the boundary. In practice, this means the result depends on the properties of the two media and on how different they are from each other.
If the second medium allows the disturbance to continue relatively easily, transmission is more noticeable. If the change at the boundary is more restrictive, reflection is more noticeable. Most boundaries are somewhere between these extremes, so the incident wave is divided into two parts rather than showing only one effect.
A useful way to think about this is that the boundary must respond to the incoming disturbance in both regions:
in the first medium, the boundary can send a disturbance back, creating reflection
in the second medium, the boundary can pass the disturbance forward, creating transmission
Because both responses can occur, it is common to observe both a returning wave and a continuing wave after the boundary interaction.
The reflected and transmitted waves are often smaller than the original incident wave. This is because the initial disturbance is no longer traveling as one single wave after it reaches the boundary. Instead, the interaction at the boundary produces more than one result.
Common physical situations
Waves on ropes or strings
A pulse moving along a rope may reach a knot where it is attached to a different rope. After the interaction, you may observe:
a pulse moving back along the original rope
a pulse moving into the second rope
This is a direct example of reflection and transmission occurring together.
Sound waves
Sound often shows partial reflection and partial transmission. A wall may reflect some sound back toward the source, while another part may pass through the wall or doorway and continue into the next space. The exact balance depends on the material at the boundary.
Light waves
At the surface of a window, some light can pass through the glass while some light is reflected from the surface.
Ray diagram for a wave (light) encountering a flat boundary. The incident ray strikes the interface, producing a reflected ray that stays in the original medium and a refracted/transmitted ray that enters the second medium, with angles measured from the normal. Source
This is why you can often see through a window and also see a faint image reflected in it. Again, both outcomes occur at the same boundary.
Interpreting boundary behavior in AP Physics 2
Questions on this topic are usually qualitative. You are expected to identify what the wave does when it reaches a boundary, not to perform a detailed calculation.
When reading a diagram or description, ask:
What is the incident wave?
Where is the boundary?
Is there a wave traveling back into the original medium?
Is there a wave traveling into the second medium?
If a wave is seen moving back from the boundary, reflection has occurred. If a wave is seen continuing into the new medium, transmission has occurred. If both are visible, then the boundary has produced both effects, which is very common.
It is also important to describe the location of each resulting wave correctly:
the reflected wave stays in the original medium
the transmitted wave appears in the second medium
In experiments, boundary behavior is often identified from snapshots taken before and after the interaction. Before the wave reaches the boundary, only the incident wave is present. After the interaction, one or two new wave motions may be visible, depending on how the boundary responds.
A strong AP response should therefore use precise language: the incident wave reaches the boundary, part may be reflected, part may be transmitted, and both reflected and transmitted waves can occur together at the same boundary.
FAQ
A transparent material does not have to transmit all of the incoming light. At the air-glass boundary, some of the wave continues into the glass, but some is sent back.
Because of that, a window can do both jobs at once: transmit enough light for you to see through it and reflect enough light for you to notice an image on the surface.
Yes. In real materials, the change from one medium to another is not always an ideal single line or surface.
A more gradual transition often reduces strong reflections because the wave changes its behavior over a region instead of all at once. A very abrupt boundary is more likely to produce a clearly noticeable reflected wave.
Some materials respond to a disturbance in more similar ways, so the wave can continue across the boundary more easily.
When the two media are a poor match, the boundary is less effective at passing the disturbance forward, so a larger fraction of the wave is reflected. Engineers often try to improve this “matching” when they want stronger transmission.
Not usually. A smooth boundary tends to produce a more regular reflected wave.
A rough boundary can send reflected wave energy in many directions instead of one clear direction. That is why a polished surface can give a strong visible reflection, while a rough surface may not produce a clear image even though reflection is still happening.
They often modify the boundary so the wave changes medium more smoothly.
Common methods include:
adding matching layers between materials
using surface coatings
designing gradual transitions instead of abrupt ones
choosing materials that respond more similarly to the wave
These methods are used in optics, acoustics, and signal transmission to help more of the wave continue forward.
Practice Questions
A wave pulse traveling along a rope reaches a boundary with a second rope. After the interaction, one pulse travels back along the first rope and another pulse travels into the second rope.
Name the two processes occurring at the boundary. [2 marks]
1 mark: identifies the returning pulse as reflection
1 mark: identifies the pulse entering the second rope as transmission
A teacher sends identical wave pulses toward two different boundaries.
At Boundary A, a strong pulse is seen in the second medium and only a weak pulse returns in the first medium.
At Boundary B, a strong pulse returns in the first medium and only a weak pulse is seen in the second medium.
(a) Describe how the wave behavior differs at Boundary A and Boundary B. [2 marks]
(b) State whether reflection and transmission can occur at the same boundary at the same time, and explain your answer using the observations above. [2 marks]
(c) For Boundary B, state where the reflected wave is located and where the transmitted wave is located after the interaction. [1 mark]
1 mark: Boundary A shows mostly transmission and only weak reflection
1 mark: Boundary B shows mostly reflection and only weak transmission
1 mark: states that reflection and transmission can occur together
1 mark: explanation that one part of the incident wave returns while another enters the second medium
1 mark: reflected wave is in the first medium; transmitted wave is in the second medium
