AP® Physics 2: Algebra-Based review sheet from Aim for Five (aimforfive.com/physics-2/units/14/14-3)
Unit 14 · Topic 14.3
14.3 Boundary Behavior of Waves and Polarization
When a wave reaches the boundary between two media, part of it reflects and part is transmitted into the new medium. The reflected part is flipped upside down if the wave is entering a medium where it moves more slowly, and stays upright if it's entering one where it moves faster. The frequency never changes at a boundary. Transverse waves can also be polarized, which can lower their intensity.
Key terms
- reflection
- transmission
- inverted pulse
- polarization
- intensity
Reflection and transmission
Tie a light rope to a heavy rope and send a pulse along the light one. At the knot, some of the pulse's energy keeps going into the heavy rope (the transmitted pulse) and some bounces back (the reflected pulse).
Whether the reflected pulse is flipped depends on the wave speed in the two media:
- Into a slower medium (light rope to heavy rope): the reflected pulse is inverted. A crest comes back as a trough.
- Into a faster medium (heavy rope to light rope): the reflected pulse is upright. A crest comes back as a crest.
- The transmitted pulse is always upright.
Fixed and free ends
A string tied to a wall is the extreme case of a slower medium: the end can't move at all. A pulse reflecting from a fixed end comes back inverted, with nearly all its energy.
A string whose end can slide freely, such as a ring on a frictionless pole, is the extreme case of a faster medium. A pulse reflects from a free end upright.
These end conditions matter again for standing waves in 14.6.
What changes and what doesn't
Crossing into a new medium never changes a wave's frequency. Each oscillation arriving at the boundary drives one oscillation on the other side.
The speed does change, because it's set by the medium. So by v = fλ, the wavelength changes in proportion to the speed. On the heavy rope, where the wave is slower, the wavelength is shorter.
Light behaves the same way. Entering glass, it slows down, keeps its frequency (and its color) and gets a shorter wavelength.
Polarization
A transverse wave on a rope can oscillate up and down, side to side, or at any angle in between. A wave that oscillates in only one plane is polarized.
Ordinary light from the Sun or a bulb is unpolarized: its electric field points in random directions perpendicular to the beam. A polarizing filter passes only the part of the light oscillating along its transmission axis. For unpolarized light, an ideal filter lets half the intensity through. Two filters with axes at 90° to each other block the light completely.
Light can also become partly polarized by reflecting off a surface such as water or a road, or by passing through certain materials. That's why polarized sunglasses cut glare from a lake.
Intensity is the power a wave carries per unit area, averaged over one period, measured in W/m². Polarizing light usually lowers its intensity, because part of the wave is removed.
Only transverse waves can be polarized. A longitudinal wave like sound oscillates along its direction of travel, so there's no sideways direction to filter. The fact that light can be polarized is evidence that light is a transverse wave.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Pulse at a rope junction
A pulse with a crest shape travels along a light rope at 20 m/s toward a knot where it joins a heavier rope, in which waves travel at 10 m/s. Describe the reflected and transmitted pulses. If a 5.0 Hz wave is sent along the same ropes instead, find its wavelength on each rope.
Show the solutionHide the solution
- Step 1: The wave is entering a slower medium, so the reflected pulse is inverted (it comes back as a trough). The transmitted pulse is upright and moves on at 10 m/s.
- Step 2: The frequency is 5.0 Hz on both ropes, because it doesn't change at a boundary.
- Step 3: Light rope: m. Heavy rope: m.
Answer: Reflected pulse inverted, transmitted pulse upright; λ = 4.0 m on the light rope and 2.0 m on the heavy rope, both at 5.0 Hz.
- Example 2Calculator allowed
Light entering water
Light with a wavelength of 600 nm in air enters water (n = 1.33). What are its frequency and wavelength in the water? Does its color change?
Show the solutionHide the solution
- Step 1: Frequency in air: Hz. It stays the same in water.
- Step 2: The speed drops by a factor of n, so the wavelength does too: nm.
- Step 3: The color we see is tied to frequency, which hasn't changed, so the light looks the same color to a diver. (A wavelength of 451 nm in air would look blue, which is why you should think of color as frequency, not wavelength.)
Answer: f = 5.00 × 10¹⁴ Hz in both; λ = 451 nm in water; the color doesn't change.
Common mistakes
- Saying the frequency changes at a boundary. Only speed and wavelength change.
- Getting the inversion rule backward. Flipped reflections happen when the wave enters a slower medium (heavier string, fixed end).
- Claiming sound can be polarized. Only transverse waves can be.
- Thinking polarization changes the frequency or speed of light. It changes the direction of oscillation and usually lowers the intensity.
On the exam
- Expect sketches: draw the reflected and transmitted pulses after they leave a junction, with the right orientation, relative widths (the slower side has the narrower pulse) and positions.
- Questions may ask what evidence shows light is a transverse wave. The answer is polarization, which longitudinal waves can't show.
Connected topics
Videos
Check yourself
4 questions on 14.3 Boundary Behavior of Waves and Polarization. Pick an answer to see if you got it, and why.
A light string is tied to a heavy string, and both are under the same tension. An upright pulse travels along the light string toward the knot. Which describes the reflected and transmitted pulses?
A pulse travels along a heavy rope toward a point where it is tied to a much lighter rope under the same tension. What is true of the reflected pulse?
A periodic wave passes from one string into a second string where the wave speed is half as large. Which describes the transmitted wave compared with the incoming wave?
Unpolarized light shines on two polarizing filters, one behind the other. The second filter is slowly rotated through 90° from the position where its axis lines up with the first filter's. What happens to the light that gets through both filters?
0 of 4 answered