AP® Physics 2: Algebra-Based review sheet from Aim for Five (aimforfive.com/physics-2/units/14/14-5)
Unit 14 · Topic 14.5
14.5 The Doppler Effect
New to AP Physics 2 since 2024–25. The Doppler effect is the change in the frequency you observe when a wave source and an observer move toward or away from each other. Moving closer, you measure a higher frequency than the source emits; moving apart, a lower one; and a faster relative speed means a bigger shift. On this exam the Doppler effect is qualitative only: you explain which way the frequency shifts and why.
Key terms
- Doppler effect
- observed frequency
- source frequency
- relative motion
- pitch
Why the frequency shifts
Picture a fire truck sending out sound crests at a steady rate. If the truck is parked, the crests spread out as evenly spaced circles. If the truck drives forward, each new crest is sent out from a little farther ahead than the last one.
In front of the truck, the crests are bunched closer together: a shorter wavelength. They still travel at the speed of sound, so more crests reach you each second. You hear a higher frequency, a higher pitch.
Behind the truck, the crests are stretched apart: a longer wavelength, fewer crests per second and a lower pitch.
The same thing happens if you move toward a parked source: you run into crests more often than if you stood still, so you measure a higher frequency.
The rules to know
- Source and observer moving toward each other: observed frequency is higher than the source's rest frequency.
- Moving away from each other: observed frequency is lower than the rest frequency.
- Moving with the same velocity (same speed, same direction): no relative motion, so the observed frequency equals the rest frequency.
- A greater relative speed gives a bigger difference between the observed and rest frequencies.
- The source itself never changes its frequency. The shift is in what the observer measures.
A siren passing by
As an ambulance approaches at a steady speed, you hear a steady pitch that is higher than its true pitch. It doesn't keep rising as it gets closer; that's a very common misconception. The sound does get louder, but loudness is amplitude, not frequency.
As it passes you, the pitch drops. As it drives away at a steady speed, you hear a steady lower pitch. If it passes very close to you, the drop is sudden. If you stand farther from the road, the drop is smoother, because only the part of the ambulance's velocity toward or away from you counts.
Doppler effect for light
Light shows the Doppler effect too. A galaxy moving away from us has its light shifted to lower frequencies, toward the red end of the spectrum (redshift). One moving toward us is blueshifted. Police radar guns and weather radar use the Doppler shift of microwaves to measure speed.
One extra you won't be tested on: if a source moves faster than the waves it makes, as a supersonic jet does, the crests pile up into a cone-shaped shock wave. When the cone sweeps past you, you hear a sonic boom.
You won't need the Doppler formula on this exam, only the direction of the shift and the reasoning behind it.
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Ranking observed frequencies
A source emits a 500 Hz tone. Rank the frequency heard by a stationary listener in each case, from highest to lowest: (A) source moves toward the listener at 20 m/s; (B) source moves toward the listener at 10 m/s; (C) source is at rest; (D) source moves away from the listener at 10 m/s.
Show the solutionHide the solution
- Step 1: Motion toward the listener raises the observed frequency, and more speed raises it more, so A is above B and both are above 500 Hz.
- Step 2: At rest (C), the listener hears exactly 500 Hz.
- Step 3: Moving away (D) lowers the frequency below 500 Hz.
Answer: A > B > C > D
- Example 2
Same velocity (classic trap)
A car and a motorcycle both drive east at 25 m/s, with the motorcycle 50 m behind the car. The car's horn emits 400 Hz. Is the frequency the motorcycle rider hears higher than, lower than or equal to 400 Hz? Explain.
Show the solutionHide the solution
- Step 1: The Doppler effect depends on the relative motion of source and observer.
- Step 2: Both move with the same velocity, so the distance between them isn't changing; there's no motion toward or away from each other.
- Step 3: With no relative motion, the rider hears the rest frequency. (This ignores wind and assumes still air.)
- Step 4: The trap is seeing two moving vehicles and assuming there must be a shift.
Answer: Equal to 400 Hz, because there is no relative motion.
- Example 3
Describing a frequency-time graph
A train blows a whistle while moving at constant speed along a straight track, passing very close to a person standing beside the track. Describe the graph of the frequency the person hears against time.
Show the solutionHide the solution
- Step 1: While the train approaches, the frequency is higher than the rest frequency and nearly constant, because the speed toward the person is constant.
- Step 2: As the train passes, the frequency drops quickly. Because the person is very close to the track, the drop is steep.
- Step 3: After it passes, the frequency stays nearly constant again, now lower than the rest frequency.
- Step 4: So the graph is a high flat section, a quick drop through the rest frequency, then a low flat section. It is not a steady rise while the train gets closer.
Answer: High and flat, a sharp drop as the train passes, then low and flat.
Common mistakes
- Thinking the pitch rises steadily as a source approaches. At constant speed, the approaching pitch is constant; it's the loudness that grows.
- Saying the source's frequency changes. The source emits the same frequency; the observer measures a different one.
- Applying a Doppler shift when source and observer move with the same velocity. With no relative motion, there's no shift.
- Spending time memorizing Doppler formulas. Only the qualitative idea is tested in this course.
On the exam
- Questions ask you to compare observed and rest frequencies, rank frequencies for several motions, or explain the shift using wavefronts bunching up or spreading out. A sketch of the crests around a moving source makes a strong justification.
- Watch for wording about relative motion: moving toward each other raises the frequency whether the source, the observer or both are moving.
Connected topics
Videos
Check yourself
4 questions on 14.5 The Doppler Effect. Pick an answer to see if you got it, and why.
An ambulance with its siren on drives past a person standing on the sidewalk at a steady speed. Compared with the frequency the siren emits, what does the person hear?
A car drives toward a wall at a constant speed while sounding its horn, which emits 400 Hz. Which frequency does the driver hear directly from the horn?
A small source emits sound at a steady frequency while moving east at constant speed through still air. How are its wavefronts spaced?
Two identical trains sound identical horns while approaching a person on a platform. Train 1 moves at 10 m/s and train 2 at 20 m/s. Which comparison of the frequencies the person hears is correct?
0 of 4 answered