The shape of the lesson
By the end of the lesson, learners can
- Bunch the wavefronts ahead: Move the source and watch the circular wavefronts crowd together in front and spread out behind.
- Approaching or receding: One formula, two signs.
- Where it matters: The same physics works from sirens to galaxies.
- Approach: fₒ = fₛ v / (v − vₛ), higher.
- Recede: fₒ = fₛ v / (v + vₛ), lower.
- Light: redshift means receding.
One picture every idea returns to
When a source moves relative to an observer, the observed frequency differs from the emitted one: this is the Doppler effect. For a source of speed vₛ emitting frequency fₛ in a medium where the wave speed is v, the observed frequency is fₒ = fₛ v / (v ± vₛ), with the minus sign for an approaching source (higher pitch) and plus for a receding source (lower pitch).
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, The pitch that shifts.. A passing siren drops in pitch the instant it goes by. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Bunch the wavefronts ahead | Move the source and watch the circular wavefronts crowd together in front and spread out behind. Project tab 3 of the lab (Doppler effect) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Approaching or receding | One formula, two signs. | Pairs |
| 21 to 30 min | Teach and check: Where it matters | The same physics works from sirens to galaxies. | Connect-Extend-Challenge |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 15 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Where it matters, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Connect-Extend-Challenge
After the new idea, each student writes three lines: how it connects to what they knew, how it extends their thinking, and what still challenges them. Pairs compare, then the challenges become the plenary.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Get the sign right: subtract the source speed in the denominator for an approaching source (which raises the frequency) and add it for a receding one. | The wave speed v is the speed in the medium and does not change; it is the spacing of the wavefronts, and hence the frequency, that changes. The syllabus formula here is for a moving source with a stationary observer. |
The Doppler effect: worksheet
6 questions, 15 marks. Written in the style of the papers; no past paper question is reproduced.
State what is meant by the Doppler effect.
A train horn emits 500 Hz and approaches a stationary observer at 25 m s⁻¹. Taking the speed of sound as 340 m s⁻¹, find the observed frequency.
The same horn (500 Hz) now recedes from the observer at 25 m s⁻¹. Find the observed frequency.
Explain why the pitch of a siren appears to drop suddenly as it passes you.
Light from a distant galaxy is found to be redshifted. State what this tells us about the galaxy.
A car sounding its 300 Hz horn approaches at 40 m s⁻¹ (speed of sound 340 m s⁻¹). Find the observed frequency.
Answer key and marking notes
- It is the change in the observed frequency of a wave ✓
- caused by relative motion between the source and the observer ✓
- fₒ = fₛ v / (v − vₛ) = 500 × 340 / (340 − 25) ✓
- = 500 × 340 / 315 ✓
- fₒ = 540 Hz ✓
- fₒ = fₛ v / (v + vₛ) = 500 × 340 / 365 ✓
- fₒ = 466 Hz ✓
- While approaching, the wavefronts bunch up, so the observed frequency is higher than emitted ✓
- As it passes and recedes, the wavefronts spread out, so the observed frequency drops below the emitted value ✓
- The wavelength is increased (frequency lowered), a Doppler shift for a receding source ✓
- So the galaxy is moving away from us, evidence for an expanding Universe ✓
- fₒ = 300 × 340 / (340 − 40) = 300 × 340 / 300 ✓
- fₒ = 340 Hz ✓
10 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
The Doppler effect occurs when a source and observer:
- Amove relative to each other
- Bhave the same speed
- Care both stationary
- Demit the same frequency
A source moving toward you sounds:
- Alower pitched
- Bunchanged
- Chigher pitched
- Dsilent
A 500 Hz source approaches at 34 m s⁻¹ (sound 340 m s⁻¹). The observed frequency is:
- A455 Hz
- B556 Hz
- C500 Hz
- D540 Hz
The same 500 Hz source recedes at 34 m s⁻¹. The observed frequency is:
- A556 Hz
- B500 Hz
- C340 Hz
- D455 Hz
In fₒ = fₛv/(v ± vₛ), the minus sign is used when the source is:
- Aapproaching the observer
- Breceding from the observer
- Cstationary
- Dfaster than sound
Redshift of light from a galaxy means the galaxy is:
- Amoving toward us
- Bstationary
- Cmoving away from us
- Dcooling
As a fast car passes you, the pitch of its engine:
- Arises suddenly
- Bdrops suddenly
- Cstays constant
- Drises then rises again
A 1000 Hz siren approaches at 20 m s⁻¹ (sound 340). The observed frequency is closest to:
- A944 Hz
- B1000 Hz
- C1020 Hz
- D1063 Hz
In the Doppler effect, the quantity that changes for the observer is the:
- Aobserved frequency
- Bspeed of the wave in the medium
- Camplitude only
- Dwave type
Doppler shift is used in speed cameras and medical scans because it measures:
- Athe temperature
- Bthe mass
- Cthe speed of a moving object
- Dthe wavelength only
Quiz key
Relative motion changes the observed frequency.
Approaching, the wavefronts bunch up, raising the frequency.
fₒ = 500 × 340/(340−34) = 500 × 340/306 = 556 Hz.
fₒ = 500 × 340/(340+34) = 500 × 340/374 = 455 Hz.
Approaching uses the minus sign, raising the frequency.
Longer wavelength (redshift) means recession.
It changes from higher (approaching) to lower (receding), so the pitch drops.
fₒ = 1000 × 340/320 = 1063 Hz.
The observed frequency changes; the wave speed in the medium does not.
The frequency shift gives the speed of the reflecting object.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.