Doppler Effect
1. Relative Motion and Frequency
Learning outcomes
- I can describe relative motion between a source and an observer.
- I can explain observed changes in frequency.
- I can distinguish between emitted and observed frequency.
- I can predict when frequency increases or decreases.
- I can describe everyday examples of the Doppler effect.
Relative Motion and Frequency
When a wave source and an observer move relative to one another, the observer may detect a frequency that is different from the frequency produced by the source. This phenomenon is called the Doppler effect.
The Doppler effect occurs with many types of waves, including:
- sound waves
- water waves
- light and other electromagnetic waves
A familiar example is the changing pitch of a siren as an emergency vehicle approaches and then passes an observer.
Relative Motion
Relative motion describes the motion of one object compared with another object.
For the Doppler effect, the two important objects are:
- the source of the waves
- the observer detecting the waves
The source might be:
- an ambulance siren
- a car horn
- a train whistle
- a loudspeaker
- a star producing light
The observer might be:
- a person
- a microphone
- a radar detector
- an ultrasound transducer
- a telescope
What matters is how the distance between the source and observer changes.
Approaching and Receding
There are two basic situations.
Approaching
The distance between the source and observer is decreasing.
Receding
The distance between the source and observer is increasing.
The Doppler effect depends on this relative motion.
A useful rule is:
approaching → observed frequency increases
receding → observed frequency decreases
The Doppler Effect
The Doppler effect is the observed change in frequency caused by relative motion between a wave source and an observer.
The source continues producing waves at its own frequency.
However, relative motion changes the rate at which wavefronts reach the observer.
Therefore, the observer can detect a different frequency.
Emitted Frequency
The emitted frequency is the frequency actually produced by the source.
It may be written as:
fₛ
where the subscript s represents the source.
For example, suppose an ambulance siren produces:
fₛ = 800 Hz
The siren continues producing approximately 800 cycles each second regardless of whether the ambulance is approaching or receding from a stationary observer.
Observed Frequency
The observed frequency is the frequency detected by the observer.
It may be written as:
fₒ
where the subscript o represents the observer.
Because of relative motion:
fₒ does not necessarily equal fₛ
For an approaching source:
fₒ > fₛ
For a receding source:
fₒ < fₛ
If there is no relevant relative motion:
fₒ = fₛ
Emitted vs Observed Frequency
| Situation | Emitted Frequency | Observed Frequency |
|---|---|---|
| No relative motion | fₛ | fₒ = fₛ |
| Approaching | fₛ | fₒ > fₛ |
| Receding | fₛ | fₒ < fₛ |
The source frequency does not have to change for the observer to hear or detect a frequency change.
This distinction is central to understanding the Doppler effect.
A Moving Sound Source
Imagine a stationary siren producing sound waves.
If the siren is not moving, its wavefronts spread outward with equal spacing in every direction in still air.
Now suppose the siren begins moving forward.
Between producing one wavefront and the next, the siren changes position.
As a result:
- wavefronts become closer together in front
- wavefronts become farther apart behind
This changes the wavelength reaching observers.
Source Moving Toward the Observer
Suppose a source moves toward a stationary observer.
Each new wavefront is emitted from a position slightly closer to the observer than the previous wavefront.
The wavefronts in front of the source become:
compressed
Therefore, the wavelength in front of the moving source becomes shorter.
Since:
v = fλ
and the speed of sound through the same stationary medium remains approximately constant:
shorter wavelength → higher observed frequency
The observer therefore detects a higher frequency.
Approaching Source
The sequence is:
source approaches
→ wavefronts become closer together
→ wavelength decreases
→ wavefronts arrive more frequently
→ observed frequency increases
For sound:
higher observed frequency → higher perceived pitch
Source Moving Away from the Observer
Now suppose the source moves away from the observer.
Each new wavefront is produced from a position farther away.
The wavefronts behind the moving source become:
more widely spaced
Therefore:
wavelength increases
With approximately constant wave speed:
longer wavelength → lower observed frequency
The observer detects a lower frequency.
Receding Source
The sequence is:
source recedes
→ wavefronts spread farther apart
→ wavelength increases
→ wavefronts arrive less frequently
→ observed frequency decreases
For sound:
lower observed frequency → lower perceived pitch
The Ambulance Example
An ambulance siren provides one of the most familiar examples of the Doppler effect.
As the ambulance approaches:
- wavefronts are compressed
- observed wavelength is shorter
- observed frequency is higher
- the siren sounds higher in pitch
As the ambulance moves away:
- wavefronts are farther apart
- observed wavelength is longer
- observed frequency is lower
- the siren sounds lower in pitch
What Happens as the Vehicle Passes?
Suppose you stand beside a road while an emergency vehicle approaches and passes.
Before it reaches you:
observed frequency > emitted frequency
After it passes:
observed frequency < emitted frequency
You therefore hear a noticeable drop in pitch around the time the vehicle passes.
The siren itself has not suddenly changed its emitted frequency.
The relative motion has changed.
Pitch and Frequency
For sound, pitch is our perception associated strongly with frequency.
Generally:
higher frequency → higher pitch
lower frequency → lower pitch
Therefore, the Doppler effect for sound is often noticed as a change in pitch.
Frequency is a physical quantity measured in hertz.
Pitch is a perception produced by the auditory system.
They are closely related but are not exactly the same concept.
The Wave Speed Does Not Increase Because the Source Moves
A common misconception is that sound travels faster in front of a moving vehicle because the vehicle is moving forward.
For ordinary sound waves in still air, this is incorrect.
The speed of sound is determined mainly by the properties of the medium.
The moving source changes the:
spacing between wavefronts
It does not simply add its speed to the speed of sound through the air.
Wave Speed, Frequency, and Wavelength
The wave equation is:
v = fλ
For sound travelling through the same region of air, v remains approximately constant.
If the source approaches:
λ decreases
so the observer encounters wavefronts more frequently.
If the source recedes:
λ increases
so the observer encounters wavefronts less frequently.
This produces the Doppler shift in observed frequency.
Example: Wavefront Spacing
Suppose a stationary siren produces sound with:
f = 500 Hz
and sound speed is:
v = 340 m/s
The wavelength is:
λ = v/f
λ = 340/500
λ = 0.68 m
If the source moves toward an observer, the wavefronts in front become closer than 0.68 m apart.
The observer therefore detects a frequency greater than 500 Hz.
Behind the source, the wavefronts are farther apart than 0.68 m, producing an observed frequency below 500 Hz.
A Stationary Source and Moving Observer
The source does not have to move.
Suppose the source is stationary while the observer moves toward it.
The observer encounters wavefronts more rapidly.
Therefore:
observer approaches source → observed frequency increases
If the observer moves away:
observer recedes from source → observed frequency decreases
The underlying principle is still relative motion between the source and observer.
Moving Source vs Moving Observer
Both situations can produce a Doppler effect, but their physical explanations differ slightly.
Moving source
Changes the spacing of wavefronts in the medium.
Moving observer
Does not change the wavelength already present in the medium but changes how rapidly the observer encounters those wavefronts.
In both cases:
approaching → higher observed frequency
receding → lower observed frequency
Both Source and Observer Moving
The source and observer can both move.
The important question remains:
Is the distance between them increasing or decreasing?
If they move toward one another:
observed frequency increases
If they move apart:
observed frequency decreases
Their individual velocities determine the size of the frequency change.
Motion Sideways to the Observer
Suppose a source moves sideways rather than directly toward or away from an observer.
Only the component of relative velocity along the line joining the source and observer produces the ordinary Doppler shift.
This component is called the:
radial velocity
Therefore, the Doppler effect tells us primarily about motion:
toward or away from the observer
rather than motion entirely sideways across the observer's view.
Predicting Frequency Changes
A simple prediction method is:
Step 1: Identify the source.
Step 2: Identify the observer.
Step 3: Ask whether the distance between them is decreasing or increasing.
If distance decreases:
approaching → higher observed frequency
If distance increases:
receding → lower observed frequency
If their separation is momentarily not changing:
no instantaneous Doppler shift from radial motion
Doppler Effect Equation for a Moving Source
For a stationary observer and a sound source moving directly toward or away from the observer, a useful equation is:
fₒ = fₛv/(v ∓ vₛ)
where:
fₒ = observed frequency
fₛ = emitted frequency
v = speed of sound
vₛ = speed of source
For an approaching source, the denominator becomes smaller:
fₒ = fₛv/(v − vₛ)
Therefore:
fₒ increases
For a receding source:
fₒ = fₛv/(v + vₛ)
Therefore:
fₒ decreases
Worked Example: Approaching Ambulance
An ambulance siren emits:
fₛ = 700 Hz
The ambulance approaches at:
vₛ = 20 m/s
Assume:
v = 340 m/s
Use:
fₒ = fₛv/(v − vₛ)
fₒ = 700 × 340/(340 − 20)
fₒ = 238000/320
fₒ ≈ 744 Hz
The observer hears approximately:
744 Hz
This is higher than the emitted frequency of 700 Hz.
Worked Example: Receding Ambulance
The same ambulance moves away at:
20 m/s.
Use:
fₒ = fₛv/(v + vₛ)
fₒ = 700 × 340/(340 + 20)
fₒ = 238000/360
fₒ ≈ 661 Hz
The observer hears approximately:
661 Hz
So:
approaching → 744 Hz
emitted → 700 Hz
receding → 661 Hz
Doppler Effect Equation for a Moving Observer
For a stationary source and an observer moving directly toward or away from it:
fₒ = fₛ(v ± vₒ)/v
where:
vₒ = observer speed
For an observer moving toward the source:
fₒ = fₛ(v + vₒ)/v
For an observer moving away:
fₒ = fₛ(v − vₒ)/v
The signs are chosen so that approaching motion increases the observed frequency and receding motion decreases it.
Worked Example: Moving Observer
A stationary source produces:
fₛ = 600 Hz
An observer moves toward the source at:
vₒ = 10 m/s
Assume:
v = 340 m/s
Then:
fₒ = 600(340 + 10)/340
fₒ = 600 × 350/340
fₒ ≈ 618 Hz
The observer detects a higher frequency because they are moving toward the source.
The Size of the Doppler Shift
The Doppler shift is the difference between observed and emitted frequency:
Δf = fₒ − fₛ
For the approaching ambulance:
fₒ = 744 Hz
fₛ = 700 Hz
Therefore:
Δf = 744 − 700
Δf = +44 Hz
A positive shift indicates an increase in observed frequency under this convention.
For a receding source, Δf would be negative.
Faster Relative Motion Produces a Larger Shift
In general, greater speed toward or away from the observer produces a larger Doppler shift.
For example, a slowly moving bicycle bell produces only a small change.
A rapidly moving racing vehicle can produce a much more noticeable change.
Therefore:
greater radial relative speed → larger frequency shift
Everyday Examples of the Doppler Effect
Common examples include:
- ambulance sirens
- police sirens
- fire-engine sirens
- train whistles
- car horns
- motorcycles
- racing vehicles
- aircraft sounds
In each case, the observed pitch changes as the source approaches and recedes.
Train Whistle Example
Imagine standing beside a railway line.
As a train approaches:
pitch sounds higher
As it passes:
pitch drops
As it moves away:
pitch sounds lower
The train whistle does not need to change its emitted frequency.
The change results from relative motion.
Racing Vehicles
The Doppler effect is often noticeable when high-speed vehicles pass a stationary observer.
As the vehicle approaches, its engine sound contains frequencies shifted upward.
After passing, those frequencies are shifted downward.
This produces the characteristic:
high → sudden drop → lower
sound heard during a pass.
Doppler Ultrasound
The Doppler effect has important medical applications.
Doppler ultrasound uses reflected ultrasound to study moving structures, especially blood.
Ultrasound is transmitted into the body.
The waves reflect from moving blood cells.
Motion changes the frequency of the reflected ultrasound.
By measuring this frequency shift, medical equipment can obtain information about blood flow.
Doppler Ultrasound Applications
Doppler ultrasound can help investigate:
- blood-flow direction
- blood-flow speed
- heart function
- blood vessels
- circulation
If blood moves toward the transducer, the reflected frequency shifts one way.
If blood moves away, it shifts the opposite way.
The equipment converts these frequency changes into useful medical information.
Radar and the Doppler Effect
Radar systems can also use Doppler shifts.
Electromagnetic waves are transmitted toward a moving object.
The waves reflect from the object and return to the detector.
If the object is moving relative to the radar system, the reflected frequency is shifted.
This can provide information about the object's:
radial velocity
Applications include:
- vehicle-speed measurement
- aircraft tracking
- weather radar
- navigation
Doppler Weather Radar
Weather radar can detect electromagnetic waves reflected by precipitation.
The Doppler shift provides information about motion toward or away from the radar.
Meteorologists can use this to investigate:
- wind motion
- storm rotation
- precipitation movement
This makes the Doppler effect important for weather monitoring and forecasting.
Astronomy and the Doppler Effect
The Doppler effect also applies to electromagnetic waves such as light.
Astronomers compare wavelengths observed from astronomical objects with known wavelengths produced by atoms.
Motion along the line of sight can shift the observed wavelengths.
If an object is moving away, its light can be shifted toward longer wavelengths.
This is called:
redshift
If an object is moving toward us, its light can be shifted toward shorter wavelengths.
This is called:
blueshift
Redshift
For visible light:
longer wavelength → toward red end of spectrum
Therefore, an object moving away can produce a Doppler shift toward longer wavelengths.
This is called:
redshift
Redshift does not necessarily mean that an object literally looks red.
Scientists often measure the shift of identifiable spectral lines.
Blueshift
An object moving toward an observer produces a shift toward shorter wavelengths.
For visible light, this is toward the blue end of the spectrum.
Therefore:
approaching astronomical object → blueshift
Again, astronomers usually measure changes in spectral lines rather than simply judging the object's apparent colour.
Measuring Stellar Motion
Suppose astronomers know the normal wavelength of a particular spectral line.
They measure the same line in light from a star.
If the observed wavelength is longer:
the star has a radial component of motion away
If the wavelength is shorter:
the star has a radial component of motion toward
The size of the shift provides information about radial speed.
Detecting Exoplanets
The Doppler effect can even help detect planets orbiting other stars.
A planet and star orbit their common centre of mass.
The star therefore moves slightly:
- toward Earth
- then away from Earth
- then toward Earth again
This produces small periodic shifts in the star's spectral lines.
Astronomers can analyze these changes to infer the presence of an orbiting planet.
This method is called the:
radial velocity method
Doppler Effect for Water Waves
The Doppler effect can also be observed with water waves.
A stationary source produces evenly spaced circular wavefronts.
If the source moves:
- wavefronts become closer together ahead of it
- wavefronts become farther apart behind it
The same basic pattern appears as for a moving sound source.
This makes water waves useful for visually demonstrating the Doppler effect.
Wavefront Diagrams
A Doppler-effect diagram often shows a moving source surrounded by wavefronts.
Look at the spacing.
Closer wavefronts
indicate shorter wavelength and higher observed frequency.
Wider-spaced wavefronts
indicate longer wavelength and lower observed frequency.
The direction in which the source is moving usually has compressed wavefronts ahead of it.
Interpreting a Doppler Diagram
Suppose a moving source travels to the right.
Wavefronts are compressed on the right.
Wavefronts are spread out on the left.
Therefore:
Observer on right:
source approaching → higher frequency
Observer on left:
source receding → lower frequency
The emitted frequency is the same source frequency for both observers.
Their observed frequencies are different.
The Observer Does Not Need to Hear the Source
The term observer does not necessarily mean a person.
An observer can be any detector.
Examples include:
- microphone
- ultrasound transducer
- radar receiver
- radio antenna
- telescope
- scientific sensor
Therefore, the Doppler effect is much broader than changes in audible pitch.
Doppler Effect vs Changing Source Frequency
Suppose a driver presses a control that actually changes the frequency produced by a siren.
That is:
a change in emitted frequency
It is not, by itself, a Doppler effect.
The Doppler effect occurs when relative motion causes:
observed frequency ≠ emitted frequency
Distinguishing these two situations is essential.
Doppler Effect vs Changing Loudness
As a vehicle approaches, its sound often becomes louder.
As it moves away, it often becomes quieter.
This change in loudness is mainly related to:
- distance
- intensity
- spreading of sound energy
The change in pitch is related to:
Doppler frequency shift
Therefore:
loudness change ≠ Doppler effect
although both can happen simultaneously.
Doppler Effect vs Wave Speed
The Doppler effect does not mean the source has changed the normal wave speed through the medium.
For sound:
- source motion changes wavefront spacing
- observer motion changes encounter rate
- the medium determines the propagation speed
For electromagnetic waves, the physics is more advanced and ultimately requires relativity for precise treatment at high speeds.
A Complete Everyday Example
An ambulance produces a siren at a constant emitted frequency.
It approaches a pedestrian.
The distance between ambulance and pedestrian decreases.
The wavefronts arriving from the approaching moving source are closer together.
The pedestrian detects:
higher observed frequency
The ambulance passes.
It now moves away.
Wavefronts reaching the pedestrian are farther apart.
The pedestrian detects:
lower observed frequency
The emitted frequency of the siren has remained essentially unchanged.
The change is caused by:
relative motion
A Complete Technology Example
A Doppler radar system transmits electromagnetic waves toward a moving vehicle.
The waves reflect from the vehicle.
Because the vehicle is moving, the reflected waves return with a shifted frequency.
The radar compares:
transmitted frequency
with:
received frequency
The frequency difference provides information about:
radial speed
The Doppler effect has therefore converted motion into a measurable frequency shift.
A Reliable Strategy for Doppler Questions
- Identify the source.
- Identify the observer or detector.
- Identify the emitted frequency.
- Determine whether the distance between source and observer is decreasing or increasing.
- If decreasing, predict a higher observed frequency.
- If increasing, predict a lower observed frequency.
- Distinguish emitted frequency from observed frequency.
- If a moving source is involved, consider wavefront compression or spreading.
- If a moving observer is involved, consider how rapidly the observer encounters wavefronts.
- Use the appropriate Doppler equation if a numerical calculation is required.
- Check whether your calculated result matches your prediction.
- For sound, relate higher frequency to higher pitch and lower frequency to lower pitch.
- Do not confuse frequency shift with changes in loudness.
- For light, connect longer wavelength with redshift and shorter wavelength with blueshift.
- Interpret the result in terms of relative motion.
Common Mistakes
Thinking the emitted frequency changes when the source moves
The source can continue emitting the same frequency while observers detect different frequencies.
Confusing emitted and observed frequency
Emitted frequency belongs to the source. Observed frequency is what the detector measures.
Thinking approaching means lower frequency
Approaching produces a higher observed frequency.
Thinking receding means higher frequency
Receding produces a lower observed frequency.
Thinking the sound travels faster in front of a moving vehicle
In still air, the source's motion changes wavefront spacing rather than simply increasing sound speed.
Confusing pitch and loudness
Pitch is strongly related to frequency. Loudness is related to sound intensity and human perception.
Thinking a louder approaching siren proves the Doppler effect
The Doppler effect specifically concerns the frequency shift.
Thinking only the source can move
A moving observer can also experience a Doppler shift.
Thinking any motion produces the same Doppler effect
Motion toward or away from the observer—the radial component—is what matters most.
Thinking redshift means a star simply looks red
Redshift is measured as a shift of wavelengths or spectral features toward longer wavelengths.
Thinking the Doppler effect applies only to sound
It also occurs with electromagnetic and other waves.
Key Terms
Relative motion — motion of one object compared with another.
Source — object or system producing waves.
Observer — person or detector receiving waves.
Doppler effect — observed frequency change caused by relative motion between source and observer.
Emitted frequency (fₛ) — frequency produced by the source.
Observed frequency (fₒ) — frequency detected by the observer.
Doppler shift — difference between observed and emitted frequency.
Approaching — relative motion that decreases the distance between source and observer.
Receding — relative motion that increases the distance between source and observer.
Wavefront — line or surface joining points of a wave in the same phase.
Wavelength (λ) — distance between corresponding points on consecutive waves.
Frequency (f) — number of wave cycles passing a point each second.
Pitch — auditory perception strongly associated with sound frequency.
Radial velocity — component of velocity toward or away from an observer.
Redshift — shift toward longer wavelengths, commonly associated with a receding astronomical source.
Blueshift — shift toward shorter wavelengths, commonly associated with an approaching astronomical source.
Doppler ultrasound — medical technique using frequency shifts of reflected ultrasound to investigate motion such as blood flow.
Doppler radar — radar technique using frequency shifts to determine radial motion.
Spectral line — particular wavelength associated with emission or absorption by atoms or molecules.
Key Takeaways
- Relative motion describes motion between a source and an observer.
- The Doppler effect is an observed change in frequency caused by relative motion.
- Emitted frequency and observed frequency are different quantities.
- The source can emit a constant frequency while an observer detects a changing frequency.
- When source and observer approach each other, observed frequency increases.
- When source and observer move apart, observed frequency decreases.
- For sound, higher observed frequency is associated with higher perceived pitch.
- Lower observed frequency is associated with lower perceived pitch.
- A moving source compresses wavefronts ahead of it and spreads wavefronts behind it.
- The wave speed through a stationary medium does not simply increase because the source moves.
- A moving observer can also experience a Doppler shift.
- The size of the Doppler shift increases with radial relative speed.
- Motion perpendicular to the line of sight does not produce the ordinary instantaneous radial Doppler shift.
- Ambulance sirens, train whistles, car horns, and racing vehicles provide everyday examples.
- Doppler ultrasound uses frequency shifts to investigate blood flow.
- Doppler radar can measure radial motion.
- Weather radar uses Doppler information to investigate motion within storms.
- Light from approaching astronomical objects can be blueshifted.
- Light from receding astronomical objects can be redshifted.
- Astronomers use Doppler shifts to measure stellar motion.
- Periodic Doppler shifts can help reveal planets orbiting other stars.
- Changes in loudness should not be confused with Doppler frequency shifts.
- The Doppler effect provides a powerful method for measuring motion using waves.
Check Your Understanding
- Define relative motion between a source and an observer.
- Explain the Doppler effect in your own words.
- Distinguish between emitted frequency and observed frequency.
- An ambulance approaches a stationary observer while emitting a constant-frequency siren. Predict how the observed frequency compares with the emitted frequency.
- The same ambulance passes the observer and moves away. Predict what happens to the observed frequency and pitch.
- Explain why wavefronts become closer together in front of a moving sound source.
- Explain why the speed of sound does not simply increase because the source moves toward an observer.
- A stationary siren produces a frequency of 600 Hz. A moving observer travels toward it. Will the observer detect a frequency greater than, equal to, or less than 600 Hz? Explain.
- An ambulance emits a 700 Hz siren and approaches at 20 m/s. Using a sound speed of 340 m/s, calculate the observed frequency for a stationary observer.
- Calculate the observed frequency when the same 700 Hz ambulance moves away at 20 m/s.
- Explain why an approaching siren can become both louder and higher in pitch, but only one of these changes is specifically the Doppler effect.
- Describe how Doppler ultrasound can provide information about blood flow.
- Explain how Doppler radar can determine whether an object is moving toward or away from a detector.
- Distinguish between redshift and blueshift and explain what each can indicate about an astronomical object's radial motion.
- A student says, "The pitch of an ambulance falls after it passes me because the driver changes the siren frequency." Evaluate this statement and use relative motion, emitted frequency, observed frequency, wavelength, and the Doppler effect to explain what actually happens.