Topic 9.29 min read
Doppler Effect: Moving Listener
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.
Choose Your Level
Beginner Level
Move toward a sounding source and you meet wave crests more quickly, so the pitch sounds higher. Move away and fewer crests reach you each second, so the pitch sounds lower.
Recommended for Class 11
Doppler Effect: Moving Listener
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.
Exam Focus
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.
Important formulas
- v = fλ
- f′ = (v + vLv)f toward
- f′ = (v − vLv)f away
Common exam traps
- 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.
Long question structure
Definition → physical cause → case diagram → derivation → sign check → numerical.
Common Mistakes
Common Mistakes
- Mistake
Use listener speed in the numerator.
- Mistake
For a stationary source, wavelength in the medium does not change.
- Mistake
Use plus for a listener moving toward and minus for moving away.
- Mistake
Do not confuse pitch with loudness or intensity.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
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.
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.
- Definition
- 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.
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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.