Doppler Effect

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The Doppler Effect

The Doppler effect is the change in observed frequency (and wavelength) of a wave due to relative motion between the source and the observer.
When a source moves towards a stationary observer, the observed frequency is higher and the wavelength is shorter.
When a source moves away from a stationary observer, the observed frequency is lower and the wavelength is longer.
The source itself emits at a constant frequency; only the observed frequency changes.
For sound, a higher frequency is heard as a higher pitch, and a lower frequency as a lower pitch.
The wave speed remains constant; frequency and wavelength change inversely (v = fλ).
Wavefront diagrams show that wavefronts are squashed in front of a moving source and spread out behind it.

The Doppler Effect for Light

The Doppler effect applies to electromagnetic waves such as light.
Light from a source moving away from the observer is redshifted: its wavelength increases and frequency decreases.
Light from a source moving towards the observer is blueshifted: its wavelength decreases and frequency increases.
Red light has a longer wavelength and lower frequency than blue light.
For a non-relativistic source (v << c), the Doppler shift is given by: Δf/f = Δλ/λ ≈ v/c.
Δλ = λ₀ − λ, where λ₀ is the observed wavelength and λ is the reference (original) wavelength.
The relative velocity is Δv = v_s − v_o; if the observer is stationary, Δv = v_s = v.
The Doppler shift has no units because it is a ratio of like quantities.

Spectral Lines and Redshift

Spectral lines from elements in a source can be compared with laboratory reference lines.
If the lines are shifted towards the red end of the spectrum, the source is moving away from Earth.
If the lines are shifted towards the blue end, the source is moving towards Earth.
Redshift is defined as the fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other.
The greater the redshift, the faster the source is moving away.
Redshift provides evidence that the universe is expanding.

Calculating Velocities from Redshift

The Doppler equation can be rearranged to find velocity: v = cΔλ/λ or v = cΔf/f.
A positive velocity indicates the source is moving towards Earth (observed frequency > reference frequency).
A negative velocity indicates the source is moving away from Earth (observed frequency < reference frequency).
Keep the minus sign in calculations to determine the direction of motion.
Wavelengths may be left in nm because the units cancel in the ratio.
The speed of light c = 3.0 × 10⁸ m s⁻¹ is given in the data booklet.

Galactic Redshift and the Expanding Universe

Almost all galaxies show redshift, meaning they are receding from Earth.
This led to the idea that the space between galaxies is expanding.
The expansion stretches light waves as they travel, shifting them towards the red end of the spectrum.
The expansion can be compared to dots on an inflating balloon: as the balloon expands, the dots move apart, but they themselves do not move.
The further a galaxy is from Earth, the greater its redshift and the faster it appears to recede.

Applications and Evidence

The discovery of Doppler redshift gave evidence for the Big Bang theory.
The Doppler effect is used to measure the rate of blood flow in patients.
It is used to find planetary orbits around distant stars.
It is used to map the expansion of the universe.
Recording the speed of sound is not an application of the Doppler effect.

Worked Example: Rotational Speed of a Galaxy

A galaxy observed edge-on shows one side blueshifted and the other redshifted.
The side with shorter wavelength (blueshift) is moving towards Earth.
The side with longer wavelength (redshift) is moving away from Earth.
The average change in wavelength is Δλ = (λ_LHS − λ_RHS)/2.
The rotational speed is found using v = cΔλ/λ, where λ is the reference wavelength.

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1.A train is moving towards a stationary observer and sounds its horn. Which row correctly shows the changes in frequency, wavelength, and pitch heard by the observer?
Easy
- AFrequency: higher, Wavelength: shorter, Pitch: higher
- BFrequency: higher, Wavelength: shorter, Pitch: lower
- CFrequency: lower, Wavelength: shorter, Pitch: lower
- DFrequency: lower, Wavelength: longer, Pitch: higher
2.What did the discovery of the Doppler redshift give scientists evidence for?
Easy
- ANewton's Third Law
- BThe formation of solar systems
- CThe Big Bang
- DBlueshift
3.Which of the following is not a use of the Doppler effect?
Easy
- AMapping the expansion of the universe
- BMeasuring the rate of blood flow in patients
- CFinding planetary orbits around distant stars
- DRecording the speed of sound
4.Which statement about redshift is true?
Easy
- ARedshift shows all galaxies are moving towards the Earth
- BRedshift shows that the space between galaxies is expanding
- CRedshift is the change in pitch of the sound waves emitted from galaxies
- DRedshift is the expansion of stars
5.Which of the following statements about the Doppler effect is correct?
Easy
- AWhen a galaxy moves towards the Earth the spectral absorption lines observed will have a longer wavelength
- BWhen a car starts to move away from an observer, the sound from the exhaust appears at a lower frequency to the observer than the driver
- CWhen a train moves towards a station, its horn will sound lower to the passengers on the platform compared to the passengers in the train
- DLight from a star moving towards the Earth is redshifted
6.Which of the following is an equation to calculate the Doppler shift of light?
Easy
- AΔf / f ≈ v / c
- BΔf / f ≈ c / v
- Cf / Δf ≈ c / v
- DΔf / f ≈ v / c²
7.In the laboratory on Earth, hydrogen emits a spectral line of wavelength 400 nm. The same line from a galaxy moving away from Earth at 0.2c is observed. What is the observed wavelength?
Medium
- A480 nm
- B320 nm
- C80 nm
- D2000 nm
8.A spectral line is observed at 530 nm in the laboratory. The same line in a galaxy receding from Earth at 3.00 × 10⁶ m/s is observed. What is the observed wavelength? (c = 3.00 × 10⁸ m/s)
Medium
- A534.7 nm
- B5.3 nm
- C535.3 nm
- D583 nm

Plus de questions

9.A star emits light of frequency f. This light is observed on Earth to have a lower frequency f'. Which row correctly describes the speed and direction of the star?
Medium
- ASpeed: ((f - f')/f)c, Direction: Towards Earth
- BSpeed: ((f - f')/f')c, Direction: Towards Earth
- CSpeed: ((f - f')/f)c, Direction: Away from Earth
- DSpeed: ((f - f')/f')c, Direction: Away from Earth
10.Which of the following statements is true about redshift?
Easy
- ARedshift led to the idea that galaxies are expanding
- BA greater redshift means a faster speed of recession
- CRedshift shows a few of the galaxies in the universe are moving away from a single point
- DRedshift causes electromagnetic waves to change frequency and speed
11.The atmosphere of the Sun rotates at speed v anti-clockwise as viewed from its north pole. What is the expression for the observed wavelength λ' of a spectral line from light emitted from the right-hand edge of the Sun as viewed from Earth?
Medium
- Aλ' = λ / (1 - v/c)
- Bλ' = λ / (1 + v/c)
- Cλ' = λ / (1 - c/v)
- Dλ' = λ / (v/c - 1)
12.The Doppler effect causes the speed of sound waves to change as the source moves.
Easy
True or false?
13.When a source of light moves away from an observer, the observed wavelength increases and the frequency decreases.
Easy
True or false?
14.Match each term with its correct description.
Medium
- Doppler effect
- Redshift
- Blueshift
- Change in observed frequency due to relative motion
- Increase in wavelength due to source moving away
- Decrease in wavelength due to source moving towards
15.Place the steps in the correct order to calculate the speed of a receding galaxy from its spectral lines.
Medium
- Measure the reference wavelength in the lab
- Measure the observed wavelength from the galaxy
- Calculate the change in wavelength Δλ
- Use Δλ/λ = v/c to find v
16.Which of the following are uses or applications of the Doppler effect? (select all that apply)
Medium
- AMeasuring the rate of blood flow in patients
- BMapping the expansion of the universe
- CFinding planetary orbits around distant stars
- DDetermining the mass of a stationary object
- ERecording the speed of sound in still air
17.A distant galaxy is observed to have its spectral lines shifted towards the red end of the spectrum. Which statements about this galaxy are correct? (select all that apply)
Medium
- AThe observed wavelength is longer than the laboratory wavelength
- BThe observed frequency is lower than the laboratory frequency
- CThe galaxy is moving away from the Earth
- DThe galaxy is moving towards the Earth
- EThe speed of the light reaching Earth is greater than c
18.The Doppler shift equation Δλ/λ ≈ v/c for light is valid under certain conditions. Which statements about this equation are correct? (select all that apply)
Hard
- AIt applies when the relative speed v is much less than the speed of light c
- BThe quantity Δλ/λ has no units
- CΔλ is the difference between the observed and reference wavelengths
- DIt can only be used for sound waves, not light
- EThe speed of the wave changes as the source moves
19.Match each observation to the correct description of the motion of the source relative to the observer.
Medium
- Observed wavelength longer than the reference wavelength
- Observed wavelength shorter than the reference wavelength
- Observed frequency equal to the reference frequency
- Observed frequency lower than the reference frequency
- Source receding (redshift)
- Source approaching (blueshift)
- Source and observer stationary relative to each other
- Source receding (redshift), lower frequency
20.Match each symbol in the Doppler shift equation Δλ/λ ≈ v/c to its correct meaning.
Medium
- Δλ
- λ
- v
- c
- Change in wavelength (observed minus reference)
- Reference (original) wavelength
- Relative velocity of the source and observer
- Speed of light
21.Place the following steps in the correct order to determine whether a distant galaxy is moving towards or away from the Earth using its spectrum.
Medium
- Observe the spectrum of light from the galaxy
- Compare the observed spectral lines with the same lines measured in the laboratory
- Identify whether the lines are shifted towards the red or blue end of the spectrum
- Conclude the direction of motion: redshift means receding, blueshift means approaching
22.Place the following steps in the correct order to calculate the speed of a receding galaxy from its spectral lines.
Hard
- Measure the reference wavelength λ in the laboratory
- Measure the observed wavelength λ₀ from the galaxy
- Calculate the change in wavelength Δλ = λ₀ − λ
- Rearrange Δλ/λ ≈ v/c to give v = cΔλ/λ and substitute the values
23.For a source of light moving away from an observer, the observed wavelength is longer than the reference wavelength.
Easy
True or false?
24.If the speed of a galaxy relative to Earth is negative, the galaxy is moving towards the Earth.
Medium
True or false?
25.The greater the distance to a galaxy, the greater its redshift tends to be.
Medium
True or false?
26.A stationary observer measures the frequency of a sound from a source moving towards them at constant speed. The source then reverses direction and moves away from the observer at the same speed. Which statement describes the change in the observed frequency?
Medium
- AThe observed frequency decreases when the source moves away compared to when it approaches.
- BThe observed frequency increases when the source moves away compared to when it approaches.
- CThe observed frequency remains the same regardless of the direction of motion.
- DThe observed frequency becomes equal to the source frequency when the source moves away.
27.A spectral line from a laboratory source has a wavelength of 500 nm. The same line from a distant galaxy is observed at 510 nm. What is the speed of the galaxy relative to Earth? (c = 3.00 × 10⁸ m/s)
Medium
- A6.00 × 10⁶ m/s
- B5.88 × 10⁶ m/s
- C3.00 × 10⁶ m/s
- D1.50 × 10⁷ m/s
28.A star is moving away from Earth at a speed of 0.01c. A spectral line that has a laboratory wavelength of 400 nm is observed from the star. What is the observed wavelength? (c = 3.00 × 10⁸ m/s)
Medium
- A404 nm
- B396 nm
- C400.04 nm
- D440 nm
29.The Doppler shift equation Δλ/λ ≈ v/c is valid only when the relative speed v is much less than the speed of light c.
Easy
True or false?
30.Place the following steps in the correct order to determine the speed of a receding galaxy using its spectrum.
Medium
- Measure the observed wavelength of a spectral line from the galaxy.
- Identify the same spectral line in the laboratory spectrum to find the reference wavelength.
- Calculate the change in wavelength Δλ = λ_observed - λ_reference.
- Use the equation v = c Δλ / λ_reference to calculate the speed.
31.State whether the galaxy is moving towards or away from the Earth.
Medium
- AAway from Earth
- BTowards Earth
- CIt is stationary relative to Earth
- DCannot be determined from the data
32.When light from a distant galaxy is observed on Earth, its spectral lines are compared with the same lines measured in a laboratory. Which statement describes the correct practical procedure for identifying a redshift?
Medium
- AThe observed wavelengths of the lines are compared with reference wavelengths measured in the laboratory; if the observed wavelengths are longer, the light is redshifted.
- BThe brightness of the galaxy's lines is compared with the brightness of the laboratory lines; a brighter line means redshift.
- CThe speed of light from the galaxy is measured and compared with the speed of light in the laboratory; a slower speed means redshift.
- DThe lines are compared with the continuous spectrum of the Sun; any dark lines indicate redshift.
33.A student uses the Doppler shift equation Δλ/λ ≈ v/c to find the speed of a distant galaxy. Which of the following are necessary for the calculation to be valid or accurate? (select all that apply)
Medium
- AThe relative speed v must be much less than the speed of light c.
- BThe observed wavelength and the reference wavelength must be measured in the same units.
- CThe galaxy must be moving exactly perpendicular to the line of sight.
- DThe reference wavelength must be measured from a laboratory source on Earth.
- EThe observed wavelength must be shorter than the reference wavelength.
34.A spectral line from a laboratory source has a wavelength of 500 nm. The same line from a distant galaxy is observed at 505 nm. What is the speed of the galaxy relative to Earth? (c = 3.00 × 10⁸ m/s)
Medium
- A3.0 × 10⁶ m/s
- B3.0 × 10⁸ m/s
- C1.5 × 10⁶ m/s
- D3.0 × 10³ m/s
35.A spectral line from a source in a laboratory has a frequency of 4.570 × 10¹⁴ Hz. The same line from a distant galaxy is observed at 4.547 × 10¹⁴ Hz. Calculate the speed of the galaxy relative to Earth and state its direction of motion. (c = 3.00 × 10⁸ m/s)
Medium
- A1.5 × 10⁶ m/s, moving away from Earth
- B1.5 × 10⁶ m/s, moving towards Earth
- C1.5 × 10⁸ m/s, moving away from Earth
- D2.3 × 10⁶ m/s, moving away from Earth
36.The stars in a distant galaxy orbit its centre. The galaxy is viewed edge-on from Earth. A spectral line from a star on the left-hand side has wavelength 656.44 nm; the same line from a star on the right-hand side has wavelength 656.12 nm. The same line measured on Earth has wavelength 656.28 nm. Calculate the rotational speed of the galaxy.
Challenge
- A7.3 × 10⁴ m/s
- B1.5 × 10⁵ m/s
- C3.7 × 10⁴ m/s
- D7.3 × 10⁶ m/s
37.A student is measuring the Doppler shift of a star using a spectrometer. To improve the accuracy of the wavelength measurements, which practical step is most appropriate?
Medium
- ACalibrate the spectrometer using known laboratory spectral lines before observing the star.
- BIncrease the speed of the star relative to Earth.
- CUse a telescope with a larger aperture to make the star appear brighter.
- DMeasure the star's spectrum only once to avoid random errors.
38.A stationary source emits sound at a constant frequency. An observer moves directly towards the source. What happens to the frequency and wavelength detected by the observer?
Easy
- AFrequency increases, wavelength decreases
- BFrequency decreases, wavelength increases
- CFrequency increases, wavelength increases
- DFrequency decreases, wavelength decreases
39.Which of the following are correct statements about the Doppler effect for sound? (select all that apply)
Medium
- AThe frequency of the source remains constant.
- BThe observed frequency is higher when the source moves towards the observer.
- CThe speed of sound in air increases when the source moves towards the observer.
- DThe observed wavelength is longer when the source moves away from the observer.
- EThe observed pitch is lower when the source moves towards the observer.
40.The Doppler effect can be observed for both sound waves and electromagnetic waves such as light.
Easy
True or false?
41.State the term for the change in observed frequency of a wave due to relative motion between the source and the observer.
Easy
42.Complete the definition of redshift.
Easy
Redshift is the fractional increase in ____ (or decrease in ____) due to the source and observer receding from each other.
43.A spectral line has a laboratory wavelength of 500 nm. The same line from a distant galaxy is observed at 505 nm. Calculate the speed of the galaxy relative to Earth. (c = 3.00 × 10⁸ m/s)
Medium
44.A source emits light of frequency 5.00 × 10¹⁴ Hz. The observed frequency is 4.99 × 10¹⁴ Hz. Calculate the speed of the source relative to the observer. (c = 3.00 × 10⁸ m/s)
Medium
45.Complete the following statements about redshift and blueshift using the correct terms.
Medium
When a source moves away from an observer, the light is ____ and the observed wavelength ____. When a source moves towards an observer, the light is ____ and the observed frequency ____.
46.A spectral line from a star has a laboratory wavelength of 486.1 nm. The same line is observed at 486.5 nm. Calculate the speed of the star relative to Earth in m/s. (c = 3.00 × 10⁸ m/s)
Hard
47.A distant galaxy is observed to have a redshift of 0.05. Calculate the speed of the galaxy relative to Earth in km/s. (c = 3.00 × 10⁵ km/s)
Hard
48.Calculate the speed of the distant galaxy in relation to the Earth in m/s. (c = 3.00 × 10⁸ m/s)
Hard
49.A spectral line from a source in a laboratory has a frequency of 4.570 × 10¹⁴ Hz. The same line from a distant galaxy is observed at 4.547 × 10¹⁴ Hz. Calculate the speed of the galaxy relative to Earth. (c = 3.00 × 10⁸ m/s)
Medium
50.A stationary source of light has a spectral line of wavelength 438 nm. The same line from a distant star moving away from us is observed at 608 nm. Calculate the speed at which the star is travelling away from Earth. (c = 3.0 × 10⁸ m/s)
Medium
51.The stars in a distant galaxy orbit its centre. The galaxy is viewed edge-on. A spectral line from a star on the left-hand side has wavelength 656.44 nm; the same line from a star on the right-hand side has wavelength 656.12 nm. The laboratory wavelength of the line is 656.28 nm. Calculate the rotational speed of the galaxy. (c = 3.0 × 10⁸ m/s)
Hard
52.A spectral line from a source in a laboratory has a frequency of 5.783 × 10¹⁴ Hz. The same line from a distant galaxy is observed at 5.791 × 10¹⁴ Hz. Calculate the speed of the galaxy relative to Earth. (c = 3.00 × 10⁸ m/s)
Medium
53.State what is meant by the Doppler effect.
Medium
54.State what is meant by redshift.
Medium
55.Explain how astronomers are able to determine that light from a distant star has undergone redshift.
Medium
56.Explain how the Doppler effect provides evidence that the universe is expanding.
Medium
57.Explain how astronomers use the Doppler effect to determine that a distant galaxy is moving away from Earth.
Hard
58.A spectral line has a laboratory wavelength of 500 nm. The same line from a distant galaxy is observed at 505 nm. Calculate the speed of the galaxy relative to Earth. (c = 3.00 × 10⁸ m/s)
Medium
- A2700000 m/s
- B3300000 m/s
- C3000000 m/s
- D3600000 m/s
59.A source emits light of frequency 5.00 × 10¹⁴ Hz. The observed frequency is 4.99 × 10¹⁴ Hz. Calculate the speed of the source relative to the observer. (c = 3.00 × 10⁸ m/s)
Medium
- A600000 m/s
- B540000 m/s
- C660000 m/s
- D720000 m/s
60.A spectral line from a star has a laboratory wavelength of 486.1 nm. The same line is observed at 486.5 nm. Calculate the speed of the star relative to Earth in m/s. (c = 3.00 × 10⁸ m/s)
Hard
- A295200 m/s
- B221400 m/s
- C270600 m/s
- D246000 m/s
61.A distant galaxy is observed to have a redshift of 0.05. Calculate the speed of the galaxy relative to Earth in km/s. (c = 3.00 × 10⁵ km/s)
Hard
- A16500 km/s
- B13500 km/s
- C18000 km/s
- D15000 km/s
62.Calculate the speed of the distant galaxy in relation to the Earth in m/s. (c = 3.00 × 10⁸ m/s)
Hard
- A1500000 m/s
- B1800000 m/s
- C1350000 m/s
- D1650000 m/s
63.A spectral line from a source in a laboratory has a frequency of 4.570 × 10¹⁴ Hz. The same line from a distant galaxy is observed at 4.547 × 10¹⁴ Hz. Calculate the speed of the galaxy relative to Earth. (c = 3.00 × 10⁸ m/s)
Medium
- A1500000 m/s
- B1350000 m/s
- C1650000 m/s
- D1800000 m/s
64.A stationary source of light has a spectral line of wavelength 438 nm. The same line from a distant star moving away from us is observed at 608 nm. Calculate the speed at which the star is travelling away from Earth. (c = 3.0 × 10⁸ m/s)
Medium
- A127600000 m/s
- B139200000 m/s
- C116000000 m/s
- D104400000 m/s
65.The stars in a distant galaxy orbit its centre. The galaxy is viewed edge-on. A spectral line from a star on the left-hand side has wavelength 656.44 nm; the same line from a star on the right-hand side has wavelength 656.12 nm. The laboratory wavelength of the line is 656.28 nm. Calculate the rotational speed of the galaxy. (c = 3.0 × 10⁸ m/s)
Hard
- A65790 m/s
- B80410 m/s
- C87720 m/s
- D73100 m/s
66.A spectral line from a source in a laboratory has a frequency of 5.783 × 10¹⁴ Hz. The same line from a distant galaxy is observed at 5.791 × 10¹⁴ Hz. Calculate the speed of the galaxy relative to Earth. (c = 3.00 × 10⁸ m/s)
Medium
- A456500 m/s
- B498000 m/s
- C415000 m/s
- D373500 m/s

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