Topic 14.5: The Doppler Effect

What Topic 14.5 requires

Topic 14.5 carries one learning objective, 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. Two essential knowledge statements sit under it, and the topic prints a boundary statement.

• 14.5.A.1 The Doppler effect describes the relationship between the rest frequency of a wave source, the observed frequency of the source, and the relative velocity of the source and the observer.
• 14.5.A.2 A greater relative velocity results in a greater measured difference between the observed and rest frequencies.
• 14.5.A.2.i For a wave source moving at the same velocity as the observer, the observed frequency is equal to the rest frequency.
• 14.5.A.2.ii For a wave source moving toward an observer, the observed frequency is greater than the rest frequency.
• 14.5.A.2.iii For a wave source moving away from an observer, the observed frequency is less than the rest frequency.

That is the whole required content of the topic. Two statements and three sub-statements.

The boundary statement, in full: Only qualitative treatments of the Doppler effect are required for AP Physics 2.

The suggested skills are 1.A (create diagrams, tables, charts, or schematics to represent physical situations), 2.C (compare physical quantities between two or more scenarios or at different times and locations in a single scenario), 3.B (apply an appropriate law, definition, theoretical relationship, or model to make a claim) and 3.C (justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws). The topic page and the Unit at a Glance table list the same four, and none of them is a calculation skill.

The CED explains what a boundary statement is on the same page it explains topic pages: boundary statements provide guidance to teachers regarding the content boundaries of the AP Physics courses, and they appear at the end of essential knowledge statements where appropriate. Unit 14 prints exactly three of them, under Topics 14.4, 14.5 and 14.9. This is one of the three.

Unit 14 is weighted at 12 to 15 percent of the multiple-choice section across a suggested 14 to 23 class periods.

Qualitative treatments only: what that sentence rules out

Take the boundary statement seriously, because it changes what you should study.

There is no Doppler equation for you to learn in this course. The CED prints none. Topic 14.5 has no relevant equation and no derived equation beside either of its essential knowledge statements. Checking the AP Physics 2 equation sheet confirms it from the other direction: the sheet carries 129 entries in seven groups, the Waves, Sound, and Optics group holds 15 of them, and no shifted-frequency expression appears in that group or anywhere else on the sheet.

So if you have seen a formula with a rest frequency multiplied by a ratio of wave speed and source or observer speed, that is real physics and it is not AP Physics 2 content. Older textbooks and a good deal of free material online still drill it. This CED, effective Fall 2024, asks for something different.

What the course requires instead is everything in 14.5.A.1 and 14.5.A.2:

• Name the three quantities the effect relates: the rest frequency of the source, the observed frequency, and the relative velocity of the source and the observer.
• Say which way the observed frequency moves in each of the three cases.
• Rank two scenarios by how large the shift is, using 14.5.A.2, which says a greater relative velocity produces a greater measured difference between observed and rest frequencies.
• Justify the ranking with a physical argument rather than a number, which is skill 3.C.

That last one is where marks are won. "Higher" is a verdict. "Higher, because the source is moving toward the observer, so 14.5.A.2.ii applies" is an answer.

One phrase in 14.5.A.1 is worth pausing on: rest frequency. It is the frequency the source emits, measured with no relative motion, and it is the quantity every comparison is made against. The observed frequency is what the detector reads. Keeping the two labels apart is most of the battle in a question with more than one observer.

The three cases, and the one people get wrong

The three sub-statements of 14.5.A.2 cover the whole qualitative picture.

The second and third rows are the familiar ones: an approaching siren sounds higher, a receding siren sounds lower. The unit's own essential questions open with exactly that scenario, asking why an ambulance siren sounds different when it is moving toward you than when it is moving away from you.

The first row is the one that catches people. 14.5.A.2.i does not say "for a source at rest". It says for a wave source moving at the same velocity as the observer, the observed frequency is equal to the rest frequency. Both can be doing 30 metres per second down a motorway and the observed frequency is unshifted, because what matters is the velocity of one relative to the other, and that is zero.

The word velocity rather than speed is deliberate. Two cars at the same speed in opposite directions are not moving at the same velocity, they are closing fast, and 14.5.A.2.ii applies.

Then 14.5.A.2 supplies the size of the effect: a greater relative velocity results in a greater measured difference between the observed and rest frequencies. So the three cases are not three separate rules. They are one continuum, with zero relative velocity in the middle and the shift growing in either direction.

That is enough to rank any set of scenarios, which is what skill 2.C asks for. Work out the relative velocity for each, note whether it is closing or separating, and order them.

One note on framing. 14.5.A.1 names a single motion variable, the relative velocity of the source and the observer, and all three sub-statements are phrased around a moving source. Beyond this course, the acoustic Doppler shift treats a moving source and a moving observer with slightly different algebra, and the two do not give identical results at the same relative speed. AP Physics 2 does not go there: the boundary statement stops at qualitative treatments, and the single variable named in 14.5.A.1 is what you reason with.

Why the pitch does not climb as the source gets closer

The CED's Instructional Approaches section includes a Conflicting Contentions activity built on this exact confusion. Students are given a train travelling at constant speed along a straight track, approaching an observer sitting on the ground near the track and sounding its horn, and asked to justify three claims.

• Claim 1: since the train is travelling at a constant speed, the pitch of the horn as measured by an observer on the ground will be constant and match the pitch of the horn as heard by an observer at rest relative to the train.
• Claim 2: even though the train is moving at a constant speed, the pitch of the horn heard by the observer on the ground will be higher than the pitch of the horn as heard by an observer at rest relative to the train.
• Claim 3: an observer on the ground will hear a higher pitch horn, and the pitch will increase as the train gets closer to the observer.

Claim 2 is the one the course's own statements support.

Claim 1 fails on 14.5.A.2.ii. The train is a source moving toward an observer, so the observed frequency is greater than the rest frequency. Constant speed does not mean no shift, it means no changing shift.

Claim 3 fails on what 14.5.A.1 and 14.5.A.2 contain. The quantities named are the rest frequency, the observed frequency and the relative velocity. Distance is not one of them. A train at constant speed has a constant relative velocity as it approaches, so the observed frequency does not change either.

Something does change as the train gets closer, and it is not the pitch. It is the loudness. 14.1.A.6.ii says the loudness of a sound increases with increasing amplitude, and 14.3.A.3.i defines intensity as the amount of power transferred per unit area, which grows as you get nearer to a source. Students hear the sound get louder and report the pitch as rising. Naming that substitution is the fastest way to stop making it.

Two clarifications keep this honest. The language of pitch is licensed by 14.2.A.1.v, which says the frequency of a sound wave is related to its pitch. And the CED's observer sits near the track rather than on it, so a fully quantitative treatment would use the component of velocity along the line between source and observer, which does vary during the pass. This course does not require that. At the level the boundary statement sets, the constant relative velocity gives a constant raised frequency until the train goes by, and a constant lowered one afterwards.

The CED's own Doppler question, worked

The AP Physics 2 CED prints 15 sample multiple-choice questions, and its second one is a Doppler question. Its alignment table lists it as skill 3.B, learning objective 14.5.A, essential knowledge 14.5.A.2, with the answer B.

The setup: a truck travels east at 25 metres per second relative to the road, emitting a loud sound at a single frequency. Four observers are placed around it. Observer A is west of the truck, behind it, moving east at 10 metres per second. Observer B is east of the truck, ahead of it, moving west at 10 metres per second. Observer C is at rest, behind the truck. Observer D is at rest, ahead of it. The question asks which observer hears the sound with the highest frequency.

The reasoning is 14.5.A.2 and nothing else: the largest relative velocity of approach gives the largest upward shift.

Only B and D hear a raised frequency, since only they have the truck coming toward them (14.5.A.2.ii). Between the two, B is also moving toward the truck, so the relative velocity is larger, and 14.5.A.2 says a greater relative velocity results in a greater measured difference. B hears the highest frequency.

Three things this question teaches about how the topic is examined.

• No numbers were used as numbers. The speeds were compared, not substituted. That is what a qualitative treatment looks like in practice, and it is why the boundary statement is not a limitation on question difficulty.
• Position matters as much as speed. A and C are behind the truck, so their relative motion is a separating one whatever their own speed. Deciding ahead-or-behind before touching the speeds is the reliable order of operations.
• The skill code is 3.B, make a claim. You are applying 14.5.A.2 as a model to reach a verdict, not deriving anything.

One rule for every kind of wave

Read 14.5.A and its essential knowledge again and notice what kind of wave they are about. They do not say sound. They say "a wave source" and "the wave", with no restriction anywhere in the topic.

So the topic as written applies to any wave with a source and an observer in relative motion, and it never separates the electromagnetic case out.

• Sound is the case the unit's essential question is built on, and the CED's own sample question uses a truck. Sound is the safe default reading.
• Nothing in the CED restricts Topic 14.5 to sound, and nothing adds a separate treatment for light. If a question puts a light source and an observer in relative motion, the three cases in 14.5.A.2 are the statements you have.
• The CED never uses the words redshift or blueshift, in Unit 14 or anywhere else. Describing the physics in its own vocabulary of rest frequency, observed frequency and relative velocity is what a rubric will reward.

The same restraint applies to the unit's fifth essential question, "what makes a sonic boom?". Essential questions are prompts for teaching, not required content, and no essential knowledge statement in Topic 14.5 or anywhere in Unit 14 mentions sonic booms or shock waves.

Where the topic does connect outward is Topic 14.2, which owns frequency itself: 14.2.A.1.ii defines frequency as the rate at which the wave repeats, 14.2.A.1.v links a sound wave's frequency to its pitch, and 14.2.A.3 prints the relationship between wavelength, speed and frequency. Topic 14.5 assumes all of that and adds relative motion on top.

What the equation sheet gives you, and how to answer without a formula

The AP Physics 2 equation sheet prints 129 entries across seven groups. Counting the Waves, Sound, and Optics group gives 15 equations, and reading all 15 turns up nothing for this topic:

$\lambda = v/f$, $n = c/v$, Snell's law, the thin-lens equation, magnification, four interference and diffraction relationships built on the path length difference $\Delta D$, the wave speed on a string, $T = 1/f$, two sinusoidal wave descriptions, and the beat frequency. That is the complete group, and no entry among them relates an observed frequency to a rest frequency.

The sheet's variable list for that group carries no Doppler symbols either: it defines $v$ as speed, $f$ as frequency or focal length, $\lambda$ as wavelength, $T$ as period, and so on.

So the answer to "what do I use for the Doppler effect on the AP Physics 2 exam" is a procedure rather than an equation.

1. Identify the rest frequency. Which frequency is the source actually emitting, or which observer would measure it unshifted?
2. Find the relative velocity of source and observer. Not their individual speeds, and not their separation. Are they closing, separating, or holding station?
3. Apply the matching sub-statement of 14.5.A.2. Closing gives a higher observed frequency, separating gives a lower one, same velocity gives no change.
4. If you are comparing scenarios, rank by relative velocity. 14.5.A.2 says larger relative velocity produces a larger difference from the rest frequency.
5. Write the justification, not just the direction. Skill 3.C is explicit that a claim needs evidence from physical principles behind it.

One nearby sheet entry gets misapplied here. $|f_{\text{beat}}| = |f_1 - f_2|$ is printed in the same group, but it belongs to Topic 14.6, where 14.6.A.6 says beats arise from the addition of two waves of slightly different frequency. Beats come from superposing two sources; the Doppler effect comes from motion. The beat equation will not tell you which way a single source's observed frequency has shifted.

How Topic 14.5 is tested

The AP Physics 2 exam runs 3 hours: 42 multiple-choice questions in 85 minutes for half the score, and 4 free-response questions in 95 minutes for the other half. A calculator is allowed on both sections. Unit 14's 12 to 15 percent weighting applies to the multiple-choice section, and the Unit 14 Progress Check in AP Classroom is listed as about 30 multiple-choice questions and 4 free-response questions.

The four suggested skills give four shapes.

• 1.A, create diagrams: draw the source, the observer, the velocity arrows, and mark which way each is going. Sketching the wave fronts bunched ahead of a moving source and spread out behind it is the standard representation. Science Practice 1 is assessed only in the free-response section, so this is Section II work.
• 2.C, compare across scenarios: the sample question above is exactly this shape, four scenarios ranked on one criterion.
• 3.B, make a claim: pick the observer, pick the higher frequency, decide whether a claim is correct.
• 3.C, justify a claim: supply the reason. The CED's Conflicting Contentions activity, with its three competing claims about a train horn, is a 3.C exercise wearing everyday clothes.

Two of the four free-response question types are natural homes for this topic. The Qualitative or Quantitative Translation question is built around the move Topic 14.5 requires, going between a verbal argument and a physical relationship. The Translation Between Representations question would pair a wave-front diagram with a statement about observed frequency.

Preparation for this topic is short, which is the point of the boundary statement. Learn the three cases in 14.5.A.2 well enough to apply them without hesitating, learn to get a relative velocity from two velocities including direction, and practise writing the justification in one sentence naming the direction of relative motion and the resulting direction of the shift. Anything spent memorising a shifted-frequency formula is spent on a different course.