🌌 Overview
What this project is, and why it's built this way
This project runs in three parts, each building directly on the last. It starts somewhere completely ordinary — a passing car, a siren, a source of sound moving relative to you — and ends somewhere extraordinary: genuine evidence, that you will handle and interpret yourself, that the Universe is expanding.
The thread connecting all three parts is relative motion. The Doppler effect only cares about the motion of a source relative to an observer — it doesn't matter, for sound, which one you call "moving." That idea seems almost trivial for sound. But push it to light, where nothing can travel faster than light itself and there is no medium for it to move "relative to," and the same simple idea stops being trivial — it becomes one of the cracks in classical physics that Einstein's relativity was built to explain. You won't derive relativity here, but you will meet the exact observation that made it necessary.
🔊 Part 1 — The Doppler Effect
Why a moving source or observer changes the frequency you detect, for both sound and light — and why the two cases turn out not to be quite the same.
🌈 Part 2 — Red Shift & Spectra
How the Doppler effect shows up in starlight as a shift in spectral lines, and what comparing two spectra can tell you about motion in space.
Where each syllabus understanding lands in the project:
| Understanding | Part |
|---|---|
| The nature of the Doppler effect for sound waves and electromagnetic waves | 1 Doppler Effect |
| Representing the Doppler effect with wavefront diagrams (source or observer moving) | 1 Doppler Effect |
| Observed frequency for sound/mechanical waves — the data-booklet equations | 1 Doppler Effect |
| Relative change in frequency/wavelength for light, Δƒ/ƒ = Δλ/λ ≈ v/c | 2 Red Shift |
| Spectral line shifts reveal the motion of stars and galaxies | 3 Investigation |
🔊 Part 1 — The Doppler Effect
What changes, what doesn't, and why it depends only on relative motion
The nature of the effect
Start with what you already know from experience: an ambulance siren sounds higher-pitched as it approaches and drops as it passes and recedes. Nothing about the siren itself changes — what changes is the relationship between the source and you.
Doppler effect
When there is relative motion between a source of waves and an observer, the frequency (and wavelength) received by the observer is different from the frequency (and wavelength) emitted by the source.
This happens for any wave — sound, water, light — but the details differ. Sound needs a medium (air) to travel through, so "the source moving" and "the observer moving" are physically distinguishable cases with (very slightly) different formulas. Light needs no medium, and its speed c is the same for every observer no matter how they're moving — which is precisely the observation that makes the Doppler effect for light subtly stranger than the Doppler effect for sound. Hold onto that thought; Part 2 comes back to it.
Wavefront diagrams — seeing why it happens
The clearest way to see why the frequency changes is to draw the wavefronts themselves — each one a circle, expanding outward from wherever the source was at the instant it was emitted. Explore the three cases below: a stationary reference case, a moving observer, and a moving source.
Wavefront explorer
- Notice that the wavefronts themselves are still circles, centred on wherever the source was when each one was emitted — the source doesn't drag the wave pattern along with it.
- What changes is the spacing between successive wavefronts on each side — bunched together ahead of a moving source (shorter wavelength, higher frequency received there) and spread out behind it (longer wavelength, lower frequency).
The equations (data booklet)
Tools — moving source, stationary observer
f ' = f · v / (v ∓ us)Use − when the source moves towards the observer (frequency increases); use + when it moves away (frequency decreases).
Tools — moving observer, stationary source
f ' = f · (v ± uo) / vUse + when the observer moves towards the source; use − when they move away. v is always the wave's own speed through its medium — never the speed of the source or observer.
A hint of things to come
Look back at the two equations above. For everyday speeds (a car, a train, even a jet aircraft), u is so much smaller than v that "source moving" and "observer moving" give almost identical answers — the distinction barely matters in practice. Sound gets away with having two slightly different formulas because it has a medium (the air) that defines a special, absolute frame of rest to measure speeds against.
Light doesn't have that luxury. There is no medium, no absolute rest frame — and experiment after experiment has confirmed that every observer measures the same value of c, regardless of how they or the source are moving. That single stubborn fact is what forced Einstein to abandon the idea of absolute time and space altogether, and build special relativity instead. The Doppler effect for light, which you'll use throughout Part 2, is already a relativistic phenomenon — we just don't need the full machinery of relativity to use its low-speed approximation.
🌈 Part 2 — Red Shift and the Comparison of Spectra
What a shifted spectral line tells you about motion in space
The Doppler effect for light
For light, the full relativistic Doppler formula is more involved than the sound-wave equations in Part 1 — but whenever the relative speed v between source and observer is much smaller than c (which is true for essentially every star and galaxy you'll meet in this project), it reduces to a very clean approximation.
Tools
Δƒ/ƒ = Δλ/λ ≈ v/cValid when v ≪ c. Δλ = λobserved − λrest. A positive Δλ (longer observed wavelength) means the source is receding — this is red shift. A negative Δλ means the source is approaching — blue shift.
Notice this is really the same idea as Part 1's moving-source equation, just written differently and simplified for v ≪ c — the physics (relative motion changes the received wavelength) hasn't changed, only the size of the effect and the fact that light's constant speed makes source-moving and observer-moving genuinely indistinguishable.
Comparing two spectra
You can't watch a single spectral line and see it shift in real time. What you actually do is compare a spectrum measured on Earth (from a lab source, or the Sun) against a spectrum received from a distant, moving object — line by line.
Explore it yourself
This tool lets you drag a recession-speed slider and watch the hydrogen line spectrum shift in real time, with the exact λobs/λrest calculation shown alongside. It's built on Google Sites, which doesn't allow itself to be embedded directly in another page — so it opens in a new tab.
Redshift Simulator (Hydrogen Spectrum)
Recession-speed slider, live spectrum shift, and the relativistic redshift calculation shown step by step.
Redshift Simulator by Dr Dan Jones, Hookean Physics (sites.google.com/view/hookean-physics).
🔭 Part 3 — Investigation: Is the Universe Expanding?
An open investigation — shifts in spectral lines provide information about the motion of stars and galaxies in space
Everything so far has been about a single source and a single observer. Now zoom out as far as it's possible to zoom: in the 1920s, Edwin Hubble and others measured the red shift of light from dozens of distant galaxies, and found something that at first looks impossible — almost every one of them is receding from us, and the further away a galaxy is, the faster it appears to be moving.
This part of the project is deliberately open. There isn't a worksheet of numbered questions with an answer key — you're given a physical model and a real dataset, and asked to build an evidence-based argument, the way an astronomer actually would.
Build it — the elastic-band Universe
Thread 5–6 washers (or paper clips) onto a chain of elastic bands, and label one your home galaxy and the rest A to E. Measure the distance from home to each of the others. Now stretch the whole chain until it's roughly twice as long, and measure those same distances again.
Plot the change in each distance against its original distance from home. Then relabel a different washer as "home" and repeat the whole measurement from scratch, on the same stretched (or freshly reset) band. (Adapted from the Institute of Physics' "Elastic Band Universe" activity.)
Read it — real recession data
Five galaxies, their distance from Earth, and the speed at which they're receding, from Doppler-shift measurements:
| Galaxy | Distance / 10²⁰ km | Speed / km s⁻¹ |
|---|---|---|
| NGC 3627 | 3.1 | 750 |
| NGC 4775 | 8.2 | 1900 |
| NGC 3147 | 13.6 | 2500 |
| NGC 6745 | 19.7 | 4250 |
| NGC 554 | 22.1 | 5200 |
Open investigation prompts
These are starting points, not a checklist to work through in order. A strong investigation will draw on both the model and the real data above, and go beyond simply reporting numbers.
- What does the gradient of a recession-speed vs. distance graph actually represent, physically — and what are its units?
- In your elastic-band model, what happened to the graph's gradient when you changed which washer was "home"? What does that tell you about whether any single galaxy — including ours — occupies a special central position?
- If speed really is proportional to distance for every galaxy you can measure, what would that imply about where all the galaxies were, much further back in time?
- The Doppler-effect equation you used in Part 2 (Δλ/λ ≈ v/c) describes light shifting because a source moves through space. Cosmological red shift is caused by space itself expanding while the light is in transit. Does your evidence so far actually let you tell these two explanations apart — or do they predict the same pattern in your data?
- The Cosmic Microwave Background. Find out what the CMBR is, and why its discovery (Penzias and Wilson, 1965) is considered independent evidence for an expanding Universe, on top of galaxy red shifts.
Extend your investigation — choose at least one
- Hubble time. If recession speed v = H₀d, and speed = distance/time, what would you get if you combined those two relationships? Using H₀ ≈ 70 km s⁻¹ Mpc⁻¹, what value does that give you — and what might it represent? What assumption about the expansion rate does this calculation quietly depend on?
- Olbers' paradox. "The sky is dark at night." Why is that actually a puzzle, if the Universe is infinite in both space and time — and how does an expanding, finitely-old Universe resolve it?
- A two-dimensional model. The elastic-band Universe is one-dimensional. Sketch (or actually build, with dots on a balloon) what a two-dimensional version would look like, and whether your "no special centre" conclusion still holds.
- If everything is the centre, why isn't matter smooth? If space itself is expanding uniformly and no galaxy occupies a special position, why do we see galaxies, clusters, and voids at all — shouldn't matter be spread perfectly evenly through the Universe rather than clumped into structures?
Track your evidence
🌠 Synthesis
Where relative motion becomes cosmology
Trace the thread back from where you finished to where you started. A moving ambulance and a stationary listener disagree about pitch because frequency depends on relative motion — that's Part 1, and it's true for any wave. Push that same idea to light, where nothing can outrun the wave itself, and it stops being a curiosity: it's a genuine crack in classical physics, one that Einstein resolved with relativity rather than a new formula.
That same relative-motion effect, applied to starlight instead of sound, becomes red shift — Part 2's tool for reading a star or galaxy's motion directly off its spectrum, without ever needing to visit it. And when that tool is turned on the whole sky at once, in Part 3, the pattern it reveals — every distant galaxy receding, faster the further away it is — becomes the central observational evidence for an expanding Universe, and for the idea that everything, everywhere, once began at a single point.
By the end of this project you should be able to give a physics-grounded answer to the driving question at the top of the page — naming exactly which piece of physics (a wavefront diagram, a shifted spectral line, a recession-speed graph) supports each part of your answer.
📝 Your Submission
How to capture and present your investigation
Written Investigation Report
A structured but open report: your elastic-band results, your graph and gradient from the real dataset, your chosen extension, and a final evidence-based discussion answering the driving question. Written in your own words, with your own diagrams.
Investigation Journal
A running log kept as you go through Parts 1–3: what you did, what you noticed, what surprised you, and how your thinking changed. Less formal than a report — closer to how a real research notebook works — finishing with the same evidence-based conclusion.