Doppler Effect & Relative Motion · Grade 12 Science
Chapter: Waves, Sound & OpticsDoppler Effect & Relative Motion
Learning goals
- I can predict sound pitch changes with specified source/observer motion.
- I can choose a sound formula and distinguish it from electromagnetic shift models.
Readings for this unit
Before this unit
Wave frequency, speed, and fractions.
Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.
Start with something to explain
Why does an approaching siren sound different without changing its own note?
Illustrative evidence case. Successive emitted fronts are closer together ahead of a moving source.
Notice and wonder
Record two observations using the stated quantities or relationships. Keep observations separate from possible causes. Write one question that a new measurement could help answer.
Why does an approaching siren sound different without changing its own note?
Your first model
Draw equal-time emission fronts and a fixed observer.
Build the language from the idea
- Doppler shift
- Change in observed frequency associated with relative motion.
- redshift
- An increase in observed wavelength relative to a reference.
Frequency observed from a moving wave source can differ from the emitted frequency. For sound, motion through the medium changes spacing between wavefronts, and observer motion changes their encounter rate. Approaching usually raises observed pitch and receding lowers it.
For a stationary observer and approaching source moving at vs below sound speed v, fobs=fsource v/(v−vs). For a receding source use v+vs in the denominator. These formulas assume a uniform stationary medium and a collinear geometry; source motion faster than sound requires a different treatment.
For observer motion and a stationary source, approaching gives fobs=fsource(v+vobserver)/v and receding gives (v−vobserver)/v. Both moving can be combined with careful signs. Sound speed is a property of the medium; it is not increased by the source’s motion.
Frequency and wavelength observed can change while the medium’s wave speed stays approximately fixed. With a moving source the emitted fronts are compressed ahead and spread behind. Pitch change is about frequency, while loudness changes depend additionally on distance, amplitude, and direction.
Electromagnetic Doppler shift is governed by relativistic relationships, not by sound’s stationary-medium formula. For low radial speeds relative to c, Δλ/λ≈vr/c is a useful approximation. A longer observed wavelength is redshift under this convention; the interpretation needs source and observer context.
Use diagrams or supplied acoustic measurements. Do not stand near traffic or moving machines to collect data. Distinguish the ideal constant-speed prediction from changing source angle, wind, reflection, or measurement uncertainty in actual sounds.
Build your understanding
Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.
Part 1 · Distinguish source emission and received frequency
The Doppler effect is a difference between emitted and received frequency caused by relative motion in the stated wave model. For a sound source moving through still air, successive fronts are emitted from progressively shifted positions. Ahead of a subsonic source their spacing shrinks; behind it spacing grows. The source can keep the same vibration frequency while a stationary receiver encounters fronts at a different rate. Distinguish emitter clock rate from receiver arrivals.
Read the visual model
Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.
Does the source need to vibrate faster for an approaching sound to have higher received frequency?
Visual reasoning — after your attempt
No. Source motion can compress front spacing even with an unchanged emission frequency.
Doppler shift concerns received frequency due to relative motion under a specified propagation model. The source can emit at a steady rate while a moving source or observer encounters altered wavefront intervals. The medium’s rest frame matters for ordinary sound.
A stationary microphone can receive a higher pitch from an approaching source even though the source oscillator has not changed its emission frequency.
Pause and explain
Does an approaching source necessarily emit at a higher frequency?
Check your reasoning after answering
No. The received wavefront timing changes; the source’s own emission rate can remain constant.
Part 2 · Use a diagram to choose signs
Sound formulas use velocities relative to the medium. A source approaching a fixed receiver shortens spacing to (v−vs)/f, so received frequency is fv/(v−vs). A moving receiver instead changes the speed at which it encounters existing fronts. Define positive approach speeds for this table rather than mixing signed coordinate velocities with an already signed formula. Draw the source, receiver, medium and propagation direction first.
Read the visual model
Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.
For f=500 Hz,v=340 m/s and approaching vs=20 m/s, what is received f?
Visual reasoning — after your attempt
500×340/320=531.25 Hz in still air with a stationary receiver.
For one-dimensional sound, approaching motion generally raises received frequency and receding motion lowers it under the usual subsonic model. Choose signs by the actual motion and verify the limit of zero motion. Different formulas may define positive source and observer velocities differently.
A moving source compresses wavefront spacing ahead and stretches it behind. A moving observer changes the encounter rate through existing wavefronts.
Pause and explain
Why should a memorized plus sign not replace a diagram?
Check your reasoning after answering
Source and observer sign conventions differ across presentations; geometry and the approach-versus-recession check determine the correct case.
Part 3 · Keep sound and light models distinct
Light in vacuum does not use a stationary air-like medium. Its relativistic Doppler shift depends on the observer–source geometry and consistent inertial-frame definitions. For longitudinal recession, fobs=femit√[(1−β)/(1+β)] with β=v/c. This differs from simply replacing sound speed by c in the moving-source formula. The low-speed approximations can be similar, but their underlying assumptions and behavior at high speed differ.
Read the visual model
Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.
For longitudinal recession at 0.60c, what fraction of emitted frequency is received?
Visual reasoning — after your attempt
√(0.40/1.60)=0.50; the observed frequency is half under the stated inertial model.
A sound formula can use source and observer speeds relative to a material medium. Light in vacuum has no ordinary sound-medium rest frame and requires a relativistic account when precision or speed demands it. Do not substitute c into an acoustic formula and call it universally valid for light.
At low speeds, some first-order approximations look similar, but their assumptions and full expressions differ.
Pause and explain
What must be specified before applying a Doppler formula?
Check your reasoning after answering
The wave type, propagation model, motion directions, and velocity reference frame must be specified.
Part 4 · Account for realistic observations
A received-frequency change does not identify a unique cause by itself. The source may change its emission rate; a moving medium can change sound propagation; source–receiver motion may have only a partial radial component. Reflections and multiple emitters can complicate the spectrum. Compare an emission reference, geometry and medium conditions before converting a shift into speed, and report the assumptions that make the calculation identifiable.
Read the visual model
Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.
Why is the full speed of a passing source not always the speed to use in a one-dimensional formula?
Visual reasoning — after your attempt
Only the appropriate motion along the source–receiver direction enters that simplified geometry; the full trajectory needs a geometric model.
Wind, changing approach angle, source acceleration, reflections, and receiver processing can alter a recorded shift. A source passing a receiver may have a changing radial velocity component. An ideal straight-line calculation predicts a controlled case, not every observed sound sequence.
Measure the geometry and source emission frequency alongside the received signal if testing the model.
Pause and explain
Why may a passing-source shift vary continuously?
Check your reasoning after answering
The component of relative motion along the propagation direction changes with geometry, rather than remaining equal to the full source speed.
Apply the whole unit · Compare an approaching and receding sound source
Illustrative source emits 500 Hz and moves directly along a line at 20.0 m/s. A receiver is stationary in still air; sound speed is 340 m/s. Use the subsonic moving-source model.
Your task
Calculate received frequency while approaching and while receding, check the zero-speed limit, and explain why the two shifts are not exactly symmetric.
What your response should show
- Define the system, quantities, units, and relevant conditions before selecting a model.
- Show intermediate calculations or a labeled evidence account, including signs or denominators.
- Explain how the supplied evidence supports the conclusion rather than reporting only an answer.
- Identify a meaningful uncertainty, model limit, or measurement needed to test the conclusion.
Response guidance — after your attempt
Approach: f′=500×340/(340−20)=531.25 Hz.
Recession: f′=500×340/(340+20)≈472.22 Hz.
At zero source speed, both expressions return 500 Hz.
The altered wavefront spacing appears in the denominator, so equal positive and negative source speeds do not produce exactly equal frequency offsets. The model assumes direct-line motion, still air, and a stationary receiver; a passing source at an angle needs the relevant geometry rather than these two constant cases.
Scientific references and source-model foundations
Parent / teacher teaching notes
Ask learners to predict higher or lower frequency before arithmetic and test the stationary limit. Keep acoustic and relativistic formulas separate. Ask the learner to explain each symbol, axis, unit and arrow before calculating. Calculated examples, supplied illustrative records and actual historical observations are labeled separately. Selected public OpenSciEd middle-school source figures are foundation examples, not complete high-school editions or an endorsement; all advanced explanations are supplied locally.
The key idea
Relative motion changes observed frequency; use a formula appropriate to the wave and medium.
Worked examples
Example 1
- fobs=600×340/(340−20).
- 204000/320.
Example 2 · Worked application
- For an approaching subsonic source, f'=fv/(v−v_s).
- f'=500×340/(340−34)≈556 Hz.
- Approach compresses wavefront spacing in front of the source.
The formula changes for moving observers or other geometries.
Example 3
- fobs=600×340/(340+20).
- 204000/360.
Example 4 · Find and fix the mistake
- Test the claim against the stated conditions: The formula changes for moving observers or other geometries.
- The source can keep its emission frequency; motion changes the frequency received.
The formula changes for moving observers or other geometries.
Example 5 · Reason from the visual model
- Light in vacuum does not use a stationary air-like medium. Its relativistic Doppler shift depends on the observer–source geometry and consistent inertial-frame definitions. For longitudinal recession, fobs=femit√[(1−β)/(1+β)] with β=v/c. This differs from simply replacing sound speed by c in the moving-source formula. The low-speed approximations can be similar, but their underlying assumptions and behavior at high speed differ.
- √(0.40/1.60)=0.50; the observed frequency is half under the stated inertial model.
Original sound/light comparison; cosmological expansion requires an additional model beyond simple local recession.
Avoid these mistakes
- Use velocities relative to the medium for sound and check geometry.
Check your understanding
Why is observed pitch lower behind a receding sound source?
Discuss the answer
Wavefronts reaching the observer are spaced farther apart, reducing encounter frequency.
Return to the phenomenon
Return to the initial case. Why does an approaching siren sound different without changing its own note? Revise your drawing or explanation using two named ideas and one stated limitation.
Compare explanations after your attempt
Wave spacing and encounter rate change; sound uses medium-relative velocities while vacuum light needs relativistic treatment.
What should we investigate next?
Which comparison would test a remaining uncertainty? State what you would change, keep comparable and measure.
Investigate, calculate and revise
Keep a first model and an evidence-supported revision. Attempt each task before opening guidance; all required explanations and supplied-data routes are available locally.
Activity 1 · Return to the opening case
Use the opening phenomenon, unit definitions and explained Parts 1–4.
Your task
Return to the initial case. Why does an approaching siren sound different without changing its own note? Revise your drawing or explanation using two named ideas and one stated limitation.
Success criteria
- Use the stated observations and appropriate units.
- Connect a labeled model with the physical/environmental mechanism.
- State assumptions and an evidence limitation.
- Explain a substantive revision or next test.
Hint
Keep object/material identity, material transfer and energy account distinct.
Response guidance — discuss after your attempt
Wave spacing and encounter rate change; sound uses medium-relative velocities while vacuum light needs relativistic treatment.
Activity 2 · Transfer to a changed case
Cover the worked answer and use the explained models, relationships and notebook.
Your task
A 600 Hz source recedes at 30 m/s from a stationary observer in still air with sound speed 330 m/s. Find received frequency and compare with the approach case at the same speed.
Success criteria
- Use the stated measurements or conditions, with correct units.
- Connect the result to the physical or environmental mechanism or evidence relationship.
- Identify the assumption, model limit or further evidence requested.
Hint
Name known quantities and conditions, show intermediate steps and check conservation.
Response guidance — discuss after your attempt
Receding:600×330/360=550 Hz. Approaching:600×330/300=660 Hz. The shifts are not symmetric about 600 in this finite-speed source model.
Words to know
- Doppler shift
- Change in observed frequency associated with relative motion.
- redshift
- An increase in observed wavelength relative to a reference.
In the real world
Use the chapter investigation to connect this unit to measured evidence and a practical decision.
Exit check
Why is observed pitch lower behind a receding sound source?
Check your explanation after answering
Wavefronts reaching the observer are spaced farther apart, reducing encounter frequency.
Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.