PhysicsChapter 9: Waves
Doppler Effect: Moving Listener
Explanation level
Overview
The Doppler effect is an apparent frequency change caused by relative motion. For a moving listener and stationary source, wavelength stays fixed while the rate at which wavefronts reach the listener changes.
Learning Outcomes
- Doppler effect is the apparent frequency change due to source–observer relative motion.
- Wave speed in stationary air remains v.
- For a moving listener and stationary source, wavelength remains λ = vf.
- Listener moving toward: f′ = (v + vLv)f, so f′ > f.
- Listener moving away: f′ = (v − vLv)f, so f′ < f.
- Higher apparent frequency gives higher pitch; lower frequency gives lower pitch.
Intermediate Level
Definition and Basic Wave Relation
The apparent change in frequency caused by relative motion between source and observer is the Doppler effect. The derivation assumes stationary air and speeds measured relative to that medium.
Listener Moving toward a Stationary Source
The source fixes the wavelength, but the listener meets wavefronts at relative speed v + vL.
Listener Moving away from a Stationary Source
The listener and wavefronts separate at relative speed v − vL, while wavelength remains unchanged.
| Listener motion | Relative wave speed | Wavelength | Apparent frequency |
|---|---|---|---|
| toward source | v + vL | unchanged | greater than f |
| away from source | v − vL | unchanged | less than f |
Listener Approaching
A stationary horn emits 600 Hz. A cyclist moves toward it at 10 m s⁻¹. If sound speed is 340 m s⁻¹, find the heard frequency.
Use the plus sign because the listener approaches.
f′ = (v + vLv)f
f′ = (340 + 10340)(600)
Final answer: f′ ≈ 618 Hz
Listener Receding
For the same horn and cyclist, find the frequency when the cyclist moves away at 10 m s⁻¹.
Use the minus sign because the listener recedes.
f′ = (340 − 10340)(600)
Final answer: f′ ≈ 582 Hz
Common Mistakes
- Use listener speed in the numerator.
- For a stationary source, wavelength in the medium does not change.
- Use plus for a listener moving toward and minus for moving away.
- Do not confuse pitch with loudness or intensity.
Short-Question Preparation
Q. Define the Doppler effect.
A. The apparent change in observed frequency due to relative motion between source and observer.
Q. Why is wavelength unchanged for a moving listener?
A. The stationary source emits wavefronts with fixed spacing in the medium.
Q. Write the approaching-listener formula.
A. f′ = (v + vLv)f.
Q. Write the receding-listener formula.
A. f′ = (v − vLv)f.
Sticky Notes
- Doppler effect is the apparent frequency change due to source–observer relative motion.
- Wave speed in stationary air remains v.
- For a moving listener and stationary source, wavelength remains λ = vf.
- Listener moving toward: f′ = (v + vLv)f, so f′ > f.
- Listener moving away: f′ = (v − vLv)f, so f′ < f.
- Higher apparent frequency gives higher pitch; lower frequency gives lower pitch.
60-Second Revision
For a stationary source, λ = vf stays fixed. A moving listener changes the arrival rate: toward gives f′ = (v + vLv)f; away gives f′ = (v − vLv)f.
Summary
The Doppler effect is an apparent frequency change caused by relative motion. For a moving listener and stationary source, wavelength stays fixed while the rate at which wavefronts reach the listener changes.
Ask-the-Tutor Modes
- Explain the Doppler effect simply.
- Choose the correct signs.
- Derive the formula.
- Solve a numerical.
- Test me with an MCQ.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.
Exam preparation
Exam Focus
Important points
- Doppler effect is the apparent frequency change due to source–observer relative motion.
- Wave speed in stationary air remains v.
- For a moving listener and stationary source, wavelength remains λ = vf.
- Listener moving toward: f′ = (v + vLv)f, so f′ > f.
- Listener moving away: f′ = (v − vLv)f, so f′ < f.
- Higher apparent frequency gives higher pitch; lower frequency gives lower pitch.
Common mistakes
- Use listener speed in the numerator.
- For a stationary source, wavelength in the medium does not change.
- Use plus for a listener moving toward and minus for moving away.
- Do not confuse pitch with loudness or intensity.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Doppler Effect: Moving Listener
Sticky Notes · Quick Revision
Key Point 1
- Doppler effect is the apparent frequency change due to source–observer relative motion.
Key Point 2
- Wave speed in stationary air remains v.
Key Point 3
- For a moving listener and stationary source, wavelength remains λ = vf.
Key Point 4
- Listener moving toward: f′ = (v + vLv)f, so f′ > f.
Ready to test yourself?
You've completed the learning section.
- 8 concept questions
- Easy → Medium → Hard
- Explanation after each answer
Exam Practice
Important Question
Q1. Define the Doppler effect.
Important Question
Q2. Why is wavelength unchanged for a moving listener?
Important Question
Q3. Write the approaching-listener formula.
Important Question
Q4. Write the receding-listener formula.
Same supplied content as this Notes page (shared canonical source).