An ambulance siren drops in pitch the instant it passes you, and the light from distant galaxies is shifted towards red. Both are the Doppler effect: motion between a wave source and an observer changes the frequency received. Master the sound Doppler equation and the language of blueshift and redshift, and you can read speed from a siren or a star.
A siren of fixed frequency is mounted on a car. The car drives towards a stationary listener, then past, then away.
Before reading: while the car is approaching, does the listener hear a higher or a lower pitch than the true siren frequency? Write your prediction and one sentence explaining why.
Motion bunches the wavefronts ahead and stretches them behind
When a source moves, it chases its own waves on one side and runs away from them on the other, so the wavefronts pile up in front (higher frequency) and spread out behind (lower frequency).
As a source moves towards an observer, each new wavefront is emitted a little closer to the previous one, so the wavefronts ahead are bunched together, shorter wavelength, higher observed frequency. Behind the source they are stretched apart, longer wavelength, lower observed frequency.
This frequency shift is the Doppler effect. An increase (approach) is called a blueshift; a decrease (recession) is a redshift. The terms come from light, frequency rising towards the blue end or falling towards the red end of the spectrum, but the same shift happens for sound (pitch up or down).
The Doppler effect is the change in observed frequency due to relative motion. Approach bunches the wavefronts → higher frequency (blueshift); recession stretches them → lower frequency (redshift). The source's true frequency and the wave speed are unchanged.
Pause, copy the highlighted explanation into your book before moving on.
Did you get this? True or false: when a source moves away from an observer, the observed frequency decreases (a redshift).
Putting a number on the shift, and choosing the right signs
We just saw why the frequency shifts. That raises a question: exactly how much does it shift for a given speed? This card answers it → the Doppler equation for sound, with a sign rule for approach and recession.
The observed frequency is the source frequency scaled by a ratio of speeds, the trick is choosing the signs so that approach raises the frequency and recession lowers it.
For sound (wave speed $v_w$ in the medium), the observed frequency is:
$$f' = f\left(\frac{v_w + v_{obs}}{v_w - v_{src}}\right)$$
Signs: use $v_{obs}$ as $+$ when the observer moves towards the source ($-$ if away); use $v_{src}$ as $+$ when the source moves towards the observer ($-$ if away). Choose signs so that approach gives a higher $f'$.
A siren of frequency $500\ \text{Hz}$ on a car moves at $30\ \text{m s}^{-1}$ directly towards a stationary observer. The speed of sound is $340\ \text{m s}^{-1}$. Find the observed frequency.
For sound, $f' = f\left(\dfrac{v_w + v_{obs}}{v_w - v_{src}}\right)$. Choose the signs so approach gives a higher $f'$ (source towards observer → subtract $v_{src}$) and recession gives a lower $f'$. The wave speed $v_w$ is fixed by the medium.
Add the highlighted equation and sign rule to your notes before the check below.
Quick check: A source moves away from a stationary observer. In the Doppler equation $f' = f\left(\dfrac{v_w}{v_w \pm v_{src}}\right)$, which sign is used and what happens to $f'$?
Pattern A, Calculate then compare
A train horn sounds at $400\ \text{Hz}$ and the train travels at $25\ \text{m s}^{-1}$. The speed of sound is $340\ \text{m s}^{-1}$, and the observer is stationary. In your book: (1) calculate the observed frequency as the train approaches; (2) calculate it as the train recedes; (3) state in one sentence which is the blueshift and which is the redshift.
Two truths, one lie: Two truths and a lie about the Doppler effect. Which statement is the lie?
Dot point: Explain the frequency shift phenomenon for sound waves and light waves (blueshift and redshift), as a source moves towards and away from an observer
The same frequency shift, applied to starlight
We just learned to calculate the shift for sound. That raises a question: the syllabus also mentions blueshift and redshift for light, how does the same idea apply to a star or galaxy? This card answers it → motion towards us shifts light to higher frequency (blue), motion away shifts it lower (red).
Light from an object moving towards us is shifted to higher frequencies (towards blue), and light from an object moving away is shifted to lower frequencies (towards red), the same Doppler logic as sound.
For light, the frequency shift works qualitatively the same way:
Source approaching → higher frequency, shorter wavelength → blueshift
Source receding → lower frequency, longer wavelength → redshift
Astronomers identify known spectral lines in a star's light and measure how far they have shifted. A redshift means the object is moving away; a blueshift means it is approaching. Most distant galaxies are redshifted, which (in Year 12) becomes key evidence that the universe is expanding. Only the quantitative calculation differs from sound; the direction of the shift follows exactly the same approach/recession rule.
For light, an approaching source gives a blueshift (higher frequency, shorter wavelength) and a receding source gives a redshift (lower frequency, longer wavelength), the same direction rule as for sound. Measuring the shift of known spectral lines reveals whether an object approaches or recedes.
Pause, copy the highlighted blueshift/redshift rule into your book before the check below.
Last check: Decide if the statement is true or false.
Light from a galaxy moving away from us is redshifted to lower frequencies and longer wavelengths.
Odd one out: Three of these describe a source moving away from an observer. Which one is the odd one out?
Dot point: Explain the frequency shift phenomenon for sound waves and light waves (blueshift and redshift), as a source moves towards and away from an observer
A fresh set drawn from this lesson's question bank, feedback shown immediately. +5 XP per correct · +25 XP all correct
Pick your answer, then rate your confidence, that tells the system what to drill next.
ApplyBand 5(4 marks) 1. A car horn emits sound at $450\ \text{Hz}$ and the car moves at $20\ \text{m s}^{-1}$ towards a stationary observer. The speed of sound is $340\ \text{m s}^{-1}$. Calculate the frequency heard by the observer, and explain whether this is a blueshift or a redshift.
1 mark: chooses $f' = f\,v_w/(v_w - v_{src})$ for approach · 1 mark: substitutes correctly · 1 mark: $f' \approx 478\ \text{Hz}$ · 1 mark: $f' > f$, so it is a blueshift (approaching source)
ApplyBand 5(3 marks) 2. An ambulance siren emits sound at $800\ \text{Hz}$ and travels at $30\ \text{m s}^{-1}$ towards a stationary observer. Taking the speed of sound as $340\ \text{m s}^{-1}$, calculate the observed frequency and comment on whether your answer is reasonable.
1 mark: correct form of the Doppler equation for an approaching source, with $(v_{\text{wave}} - v_{\text{src}})$ in the denominator · 1 mark: $f' = 800 \times 340/310$ · 1 mark: $f' = 877\ \text{Hz}$, higher than the emitted frequency as expected for an approaching source
Dot point: Solve frequency shift phenomenon problems for sound using the Doppler equation
AnalyseBand 6(3 marks) 3. Explain, in terms of wavefronts, why the frequency observed from a moving source differs from the frequency it emits, and describe how the same effect appears for light as blueshift and redshift.
1 mark: the source moves between emitting successive wavefronts, so the spacing of the arriving wavefronts changes · 1 mark: approaching means bunched wavefronts, so a shorter observed wavelength and higher observed frequency, and the reverse for receding · 1 mark: for light this appears as a shift towards the blue end when approaching and the red end when receding
Dot point: Explain the frequency shift phenomenon for sound waves and light waves (blueshift and redshift), as a source moves towards and away from an observer
MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set from the lesson bank.
Q1 (4 marks): The observer is stationary and the source is approaching, so we subtract the source speed in the denominator: $f' = f\left(\dfrac{v_w}{v_w - v_{src}}\right) = 450\left(\dfrac{340}{340 - 20}\right) = 450 \times \dfrac{340}{320} = 478\ \text{Hz}$ (to 3 significant figures). Because the observed frequency ($478\ \text{Hz}$) is higher than the emitted frequency ($450\ \text{Hz}$), this is a blueshift: the source is moving towards the observer, bunching the wavefronts so they arrive more frequently and the pitch is raised.
Q2 (3 marks): For a source approaching a stationary observer the source speed is subtracted in the denominator, because each successive wavefront is emitted from a position closer to the observer and the wavefronts bunch up: $f' = f \dfrac{v_{\text{wave}}}{v_{\text{wave}} - v_{\text{src}}}$. Substituting, $f' = 800 \times \dfrac{340}{340 - 30} = 800 \times \dfrac{340}{310} = 877\ \text{Hz}$ (3 s.f.). The answer is reasonable: it is higher than the emitted $800\ \text{Hz}$, which is what must happen for an approaching source, and the increase of about $10\%$ is consistent with the source moving at roughly $9\%$ of the speed of sound. A result below $800\ \text{Hz}$ would have indicated the wrong sign in the denominator.
Q3 (3 marks): The source emits wavefronts at a steady rate, but between emitting one wavefront and the next it has moved. Each new wavefront is therefore centred on a slightly different point. Ahead of the source the wavefronts are emitted successively closer to the observer, so they are bunched together: the observed wavelength is shorter and, since the wave speed through the medium is unchanged, the observed frequency is higher. Behind the source the opposite happens: each wavefront is emitted from further away, so the wavefronts are stretched apart, the observed wavelength is longer and the observed frequency is lower. It is essential to note that the source's emitted frequency has not changed at all; only the spacing of the wavefronts reaching the observer has. For light the same geometry applies. A source approaching the observer has its wavelengths shortened, moving the observed spectrum towards the blue end: a blueshift. A source receding has its wavelengths lengthened, moving the spectrum towards the red end: a redshift. Measuring the shift in the spectral lines of a distant galaxy therefore reveals whether it is approaching or receding.
You can now explain the Doppler effect, choose the right signs in the sound Doppler equation, calculate observed frequencies, and classify shifts as blueshift or redshift for sound and light. That completes Focus Area 2, Waves: you have travelled from describing waves to reflection, refraction, diffraction, interference, standing waves and the Doppler effect.
↩ Back to focus-area hubAt the start you predicted the pitch of an approaching siren. It sounds higher than the true frequency: the source chases its own wavefronts, bunching them so they arrive more often, a blueshift. If you predicted lower, revisit Card 1, the drop to a lower pitch happens only after the source has passed and begins receding.
A short spaced-retrieval set, mixing this lesson with earlier ones. It gets harder to guess and easier to remember.
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