Key Idea: The Doppler effect is one idea seen in two forms: when a wave source moves toward or away from you, the wave you receive is shifted. For sound the pitch changes — higher coming, lower going. For light the wavelength changes — blueshift (shorter) approaching, redshift (longer) receding.
Sound
- Towards: higher pitch
- Away: lower pitch
- Source or observer can move
Light
- Δλ/λ ≈ v/c (v ≪ c)
- Redshift: receding
- Blueshift: approaching
Read it
- Along the line: a step as it passes
- Rotating star: both shifts
- Spectral lines show the motion
The source itself never changes; only what the observer measures does. It is examined on both papers. Paper 1A tends to be quick: which way the pitch shifts, the shape of the heard-frequency graph as a source passes, or whether a galaxy is approaching or receding. Paper 2 asks you to explain a shift, for sound or light, and to calculate a speed with Δλ/λ = v/c (a star, a galaxy, or a rotating star's edge).
Key formulas
The light equation carries the data-booklet badge. For sound at SL you describe the shift; the sound equations are HL only.
- change in wavelength, observed − lab (m) — written Δλ
- the source's true (laboratory) wavelength (m)
- change in frequency, observed − lab (Hz) — written Δf
- the source's true (laboratory) frequency (Hz)
- speed of the source toward or away from us (m s⁻¹)
- the speed of light, 3.0 × 10⁸ m s⁻¹
A moving source bunches the wavefronts ahead of it and stretches them behind; a moving observer meets them more or less often. For light the shift is a tiny fraction of the wavelength: Δλ/λ ≈ v/c.
Sound vs light Doppler
| Doppler for SOUND | Doppler for LIGHT | |
|---|---|---|
| What shifts | The pitch (frequency) you hear | The wavelength (and frequency) you observe |
| Equation | none at SL: describe the shift | Δλ/λ = Δf/f ≈ v/c |
| Approaching | Higher pitch | Blueshift — λ shorter (toward blue) |
| Receding | Lower pitch | Redshift — λ longer (toward red) |
| Where tested | Sirens, horns; passing-source graph | Stars, the Sun's edges, galaxies |
| Key reminder | the speed of sound does not change; the pitch steps as it passes along the line | Δλ is the change, not the whole λ; valid for v ≪ c |
Approaching vs receding — read off the direction
| Motion | Wavefronts | Sound (pitch) | Light (wavelength) |
|---|---|---|---|
| Approaching (toward you) | Bunched up → shorter wavelength | Higher | Blueshift — λ shorter, Δλ negative |
| Receding (away from you) | Stretched out → longer wavelength | Lower | Redshift — λ longer, Δλ positive |
Red = Receding (away, longer λ); blue = approaching (toward, shorter λ). For sound, moving towards (source or observer) means a higher pitch, away a lower one. The source's own frequency never changes.
One edge of a spinning star (or the Sun) turns toward us → that edge is blueshifted (shorter λ). The opposite edge turns away → redshifted (longer λ). The edge speed v is the surface rotation speed, found from the shift of one edge — not the gap between the two.
Worked exam-style questions
A fire engine drives directly towards a stationary observer with its siren on. Explain, in terms of wavefronts, why the observer hears a higher frequency than the siren emits.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Next:
A cyclist rides at steady speed along the line from loudspeaker X towards loudspeaker Y. X emits 520 Hz and Y emits 480 Hz. Explain why she can hear both at the same frequency.
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Next:
A spectral line with a laboratory wavelength of 500.0 nm is observed at 508.0 nm in the light from a distant galaxy. Find the galaxy's speed relative to Earth, and state its direction of motion. (c = 3.0 × 10⁸ m s⁻¹.)
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Next:
A line that is 589.00 nm in the laboratory is observed at 588.80 nm in light from one edge of a rotating star. State whether that edge is approaching or receding, and find its speed. (c = 3.0 × 10⁸ m s⁻¹.)
Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Important: In Δλ/λ, Δλ is the change (observed − laboratory), not the observed wavelength itself.
Quick self-check
Tap each card to reveal the answer.
A sound source moves toward you — higher or lower pitch, and why? Higher pitch — the wavefronts bunch up ahead of the source, so more reach you each second.
Shape of the heard-frequency graph as a sound source passes? High-flat → sharp step down → low-flat, crossing the true pitch at the instant it passes. This is for motion along the line through you; passing at a distance, the drop is quick but smooth.
A galaxy's light is redshifted — toward or away, and what does it imply? Away (receding) — λ is stretched longer (red = receding). Almost all distant galaxies are redshifted, evidence the Universe is expanding.
What does Δλ mean in Δλ/λ = v/c? The change in wavelength: observed − laboratory — not the whole observed wavelength. Divide the small change by the original λ.
Why does a rotating star show two shifts at once? One edge turns toward us (blueshift, shorter λ) and the opposite edge turns away (redshift, longer λ); both at the surface rotation speed.
Does the source's own frequency change in the Doppler effect? No. The source always emits the same f (or λ). Only the observed value changes, because of the relative motion.
Exam tips
Exam tips
- Sound: moving towards (source or observer) means a higher frequency heard, away a lower one. The source's own frequency never changes.
- The heard-frequency graph of a passing source is high-flat, a sharp step down, then low-flat — a step when the source moves along the line through the listener (passing at a distance, the drop is quick but smooth).
- Light: rearrange Δλ/λ = v/c to v = (Δλ ÷ λ) × c. Use the change Δλ (observed − lab) on top, NOT the whole observed wavelength.
- Keep λ and Δλ in the same units (e.g. both nm) — they cancel in Δλ/λ; only c must be in m s⁻¹.
- Red = Receding (away, longer λ); blue = approaching (toward, shorter λ). A rotating star shows BOTH at once, one edge each.
- Δλ/λ = v/c is valid only when v is much smaller than c — that is why everyday sources give an undetectable light shift (v/c ~ 10⁻⁷) but fast galaxies give a measurable one.
- In every case the source emits one fixed frequency/wavelength; it is the relative motion that changes what the observer measures.