The Doppler Effect
Use emitted wavefronts and encounter rates to explain qualitative Doppler shifts.
AP Physics 2 Topic 14.5 · College Board CED printed p. 118 / PDF p. 125 · See this topic in the course outline
Doppler shift is about how frequently wavefronts reach an observer. Follow both the source and the observer relative to the medium.
Before you start
- Wavefronts
- Frequency
- Relative motion
Approach, recession, and the medium
The rest frequency is how often the source emits cycles in its own repeating operation. The observed frequency is how often cycles reach the observer. A source approaching a stationary listener emits successive sound wavefronts from closer positions, crowding the fronts ahead of it: the listener hears higher frequency. Behind a receding source the fronts are farther apart, so the listener hears lower frequency. The sound speed relative to still air is set by the air, not by the speed of the siren.
A moving observer changes the rate at which it meets fronts: moving toward a stationary source raises the observed frequency; moving away lowers it. For straight-line sound propagation, source motion changes front spacing and observer motion changes encounter rate. Both can act at once. An observer and source moving together with the same velocity relative to the medium have equal observed and rest frequencies in this model, even though the fronts are not necessarily symmetric in the air frame.
For a given source/observer arrangement, increasing the approach or recession speed strengthens the shift. Do not use only distance: a nearby source with no radial relative motion need not be shifted. “Greater relative speed gives a larger shift” is a qualitative trend for a specified arrangement; sound source and observer velocities relative to the medium matter separately, so two different arrangements with the same closing speed need not have identical shifts. The ordinary subsonic model also cannot describe a source outrunning its wavefronts; shocks require another model. AP Physics 2 requires qualitative Doppler reasoning, not memorized Doppler formulas. For light, approach produces a higher observed frequency (blueshift) and recession a lower one (redshift); a quantitative relativistic treatment is beyond this lesson.
A source and a listener both move
A siren moves right toward a listener. The listener moves left toward the siren, both subsonic in still air. Predict the heard pitch and compare with a listener standing still.
Sketch emission fronts closer together ahead of the moving source.
Equal-time wavefront construction. Blue circles are successive fronts observed at one common time; black dots are their earlier emission centers. The source moves right at 24 illustrative distance units/s, below sound speed 36 units/s, and emits once each second. Ahead of it, successive fronts are 12 units apart; behind it, 60 units apart. A stationary source would give 36-unit spacing. S is source and O observer. In the left panel the observer also moves left and crosses approaching fronts faster. Why this step? The source advances between emissions, reducing forward front spacing.
The listener moving left encounters those approaching fronts more frequently than a stationary listener.
Why this step? Observer motion changes encounter rate relative to the air.
Both effects raise observed frequency; the moving listener hears a higher frequency than the stationary one at the same place.
Why this step? Combining physical effects avoids an unjustified single relative-speed shortcut.
Answer and check
The observed frequency exceeds the rest frequency and exceeds that heard by the stationary comparison listener.
Try it from memory
Write your answer and reason before opening the worked answer. Your self-assessment is a study decision; it is not an automatically graded score.
Question 1
A siren and listener travel together at the same velocity in still air, with fixed separation. Is their observed frequency shifted?
Worked answer and reason
No in the straight-line sound model: source front-spacing and observer encounter-rate changes cancel.
Equal velocities produce equal observed and rest frequency, even though both move relative to air.
Question 2
A parked siren and parked listener are close together. Another parked listener is far away. Must the far listener hear lower pitch?
Worked answer and reason
No. Distance alone can reduce intensity or delay arrival, but without relative radial motion the frequencies match.
Doppler is an arrival timing effect from motion, not a distance-based pitch rule.
JavaScript enables saved drafts and self-assessment. You can always work on paper.
Catch the tempting mistake
- A moving siren makes sound travel faster through the air.
- Ordinary sound speed relative to the air is a medium property; the source changes the spacing of emitted fronts.
Put it to work
Give the physical reason as well as the calculation. The worked solutions are on a separate page.
- Problem 9 · mixed
- Problem 10 · mixed
Scientific calculator workspace
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Scientific calculator
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For the teacher
- Use source emission dots separated by equal times; compare moving source with moving observer. Quantitative sound Doppler expressions are enrichment, not required assessment.
Source objectives and scope
- 14.5.A — Describe the properties of a wave based on the relative motion between the source of the wave and the observer of the wave.
Only qualitative treatments of the Doppler effect are required for AP Physics 2.
Suggested skills are teaching guidance. The course applies all science practices across its objectives.
Science references for this teaching
- AP Physics 2 Course and Exam Description, official Unit 14 — Official topic/LO/EK scope and boundaries; local pinned source pages 117–134, equations visually checked on 118,120,130,132,134.
- OpenStax University Physics 1, Energy and Power of a Wave — Verification of fixed-amplitude mechanical-wave frequency scaling and distinction from electromagnetic intensity.
- OpenStax University Physics 1, Interference of Waves — Linear superposition and pointwise addition model.
- OpenStax University Physics 3, Single-Slit Diffraction — Verification of aperture minima and small-angle conditions.
- OpenStax University Physics 3, Interference in Thin Films — Verification of reflection phase and normal-incidence thin-film paths.
Related source reading
These alternative explanations and examples retain their source context. Draft placement does not add accepted exam coverage.
- A reflected-ultrasound model · source context; placement review pending
Glossary and deeper reading · 3 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Wavefront
A wavefront is a surface joining points of equal wave phase at a given time. Rays are perpendicular to wavefronts in the uniform isotropic ray model used here. For example, a distant source can be approximated by nearly plane wavefronts over a small region.
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Frequency
Frequency is the number of complete repeating cycles per unit time. It is measured in hertz, meaning cycles per second, and is the reciprocal of the period. For example, a vibrating string with a higher frequency produces more cycles each second.
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Velocity
Velocity describes how position changes with time and includes direction. Instantaneous velocity describes one moment, while average velocity is displacement divided by elapsed time. For example, a car turning a corner can change velocity while maintaining the same speed.