Topic 9.29 min read
Doppler Effect: Moving Source
For a moving source and stationary listener, the source changes the spacing of wavefronts: approach shortens wavelength and raises apparent frequency, while recession lengthens wavelength and lowers it.
Choose Your Level
Beginner Level
A moving source bunches wave crests in front and spreads them behind. A listener ahead hears a higher pitch, while a listener behind hears a lower pitch.
Recommended for Class 11
Doppler Effect: Moving Source
Overview
For a moving source and stationary listener, the source changes the spacing of wavefronts: approach shortens wavelength and raises apparent frequency, while recession lengthens wavelength and lowers it.
Learning Outcomes
- A source moving toward a listener shortens wavelength ahead of it.
- Approaching source: λ′ = v − vSf and f′ = (vv − vS)f.
- A source moving away lengthens wavelength behind it.
- Receding source: λ′ = v + vSf and f′ = (vv + vS)f.
- The sound speed relative to stationary air remains v.
- Approach raises pitch; recession lowers pitch.
Intermediate Level
How Source Motion Changes Wavelength
In one period T = 1f, a source moves distance vST. Each new crest is emitted from a shifted position, changing crest spacing while the crests themselves still travel through air at speed v.
Source Moving toward a Stationary Listener
Because vv − vS is greater than one, f′ > f.
Source Moving away from a Stationary Listener
Because vv + vS is less than one, f′ < f.
| Source motion | Wavelength | Denominator | Frequency |
|---|---|---|---|
| toward listener | shorter | v − vS | higher |
| away from listener | longer | v + vS | lower |
Textbook Example 9.2
A 354 Hz source recedes from a stationary observer at 22 m s⁻¹. If v = 332 m s⁻¹, find the apparent frequency.
Receding source: f′ = (vv + vS)f
f′ = (332332 + 22)(354)
Final answer: f′ = 332 Hz
Textbook Assignment 9.2 Solved
A bus horn emits 500 Hz while the bus moves at 20 m s⁻¹. Find the frequencies heard by a stationary roadside observer as the bus approaches and recedes. Use v = 340 m s⁻¹.
Approaching: f′ = (340340 − 20)(500) = 531.25 Hz
Receding: f′ = (340340 + 20)(500) = 472.22 Hz
Final answer: About 531 Hz approaching and 472 Hz receding
Common Mistakes
- Source speed belongs in the denominator.
- Use v − vS for approach and v + vS for recession.
- Wave speed remains v; source motion changes wavelength.
- The subsonic formula assumes vS is less than v.
Short-Question Preparation
Q. Why does a moving source change wavelength?
A. It emits successive crests from different positions.
Q. Write the approaching-source formula.
A. f′ = (vv − vS)f.
Q. Write the receding-source formula.
A. f′ = (vv + vS)f.
Q. What happens to wavelength ahead of the source?
A. It becomes shorter, so the frequency heard ahead is higher.
Sticky Notes
- A source moving toward a listener shortens wavelength ahead of it.
- Approaching source: λ′ = v − vSf and f′ = (vv − vS)f.
- A source moving away lengthens wavelength behind it.
- Receding source: λ′ = v + vSf and f′ = (vv + vS)f.
- The sound speed relative to stationary air remains v.
- Approach raises pitch; recession lowers pitch.
60-Second Revision
A moving source shifts crest spacing. Toward: λ′ = v − vSf and f′ = vf/(v − vS). Away: λ′ = v + vSf and f′ = vf/(v + vS).
Summary
For a moving source and stationary listener, the source changes the spacing of wavefronts: approach shortens wavelength and raises apparent frequency, while recession lengthens wavelength and lowers it.
Ask-the-Tutor Modes
- Explain the Doppler effect simply.
- Choose the correct signs.
- Derive the formula.
- Solve a numerical.
- Test me with an MCQ.
Exam Focus
Exam Focus
Important points
- A source moving toward a listener shortens wavelength ahead of it.
- Approaching source: λ′ = v − vSf and f′ = (vv − vS)f.
- A source moving away lengthens wavelength behind it.
- Receding source: λ′ = v + vSf and f′ = (vv + vS)f.
- The sound speed relative to stationary air remains v.
- Approach raises pitch; recession lowers pitch.
Important formulas
- λ′ = v − vSf toward
- f′ = vf/(v − vS) toward
- λ′ = v + vSf away
- f′ = vf/(v + vS) away
Common exam traps
- Source speed belongs in the denominator.
- Use v − vS for approach and v + vS for recession.
- Wave speed remains v; source motion changes wavelength.
- The subsonic formula assumes vS is less than v.
Long question structure
Definition → physical cause → case diagram → derivation → sign check → numerical.
Common Mistakes
Common Mistakes
- Mistake
Source speed belongs in the denominator.
- Mistake
Use v − vS for approach and v + vS for recession.
- Mistake
Wave speed remains v; source motion changes wavelength.
- Mistake
The subsonic formula assumes vS is less than v.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
A source moving toward a listener shortens wavelength ahead of it.
Approaching source: λ′ = v − vSf and f′ = (vv − vS)f.
A source moving away lengthens wavelength behind it.
Receding source: λ′ = v + vSf and f′ = (vv + vS)f.
For a moving source and stationary listener, the source changes the spacing of wavefronts: approach shortens wavelength and raises apparent frequency, while recession lengthens wavelength and lowers it.
- Definition
- For a moving source and stationary listener, the source changes the spacing of wavefronts: approach shortens wavelength and raises apparent frequency, while recession lengthens wavelength and lowers it.
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Exam Practice
Important Question
Q1. Why does a moving source change wavelength?
Important Question
Q2. Write the approaching-source formula.
Important Question
Q3. Write the receding-source formula.
Important Question
Q4. What happens to wavelength ahead of the source?