The Doppler Effect closes the C-block of IB Physics HL by linking wave physics to astrophysics, medical imaging and traffic enforcement. SL students need the qualitative idea (approaching $\Rightarrow f' > f$, receding $\Rightarrow f' < f$) and the simple light-Doppler approximation $\Delta f / f = v/c$. HL adds the quantitative sound formulas for moving source and moving observer, where the asymmetry between the two cases is one of the most-examined details in Topic C.5.
This cheatsheet condenses every Topic C.5 formula and exam trap into one revision sheet — wavefront diagrams, the four sound-Doppler cases, redshift vs blueshift, and the radar / ultrasound / Hubble applications. The most common HL pitfalls — mixing the source and observer formulas, getting the sign wrong, missing the factor of 2 in the radar formula, applying the simple $v/c$ relation to sound — are flagged in red.
§1 — The Doppler Effect C.5 SL + HL
Definition
The Doppler effect: the observed frequency of a wave changes when the source and observer move relative to each other.
- Approaching $\Rightarrow f' > f$ (higher frequency, shorter wavelength).
- Receding $\Rightarrow f' < f$ (lower frequency, longer wavelength).
- The speed of the wave in the medium is unchanged by source or observer motion.
Wavefront summary
| In front of source | Behind source | |
|---|---|---|
| Wavelength | Compressed ($\lambda' < \lambda$) | Stretched ($\lambda' > \lambda$) |
| Frequency | Higher ($f' > f$) | Lower ($f' < f$) |
| Speed of sound | Same as stationary | Same as stationary |
§2 — Doppler Formulas for Sound C.5 HL Additional
Moving source (HL)
Moving observer (HL)
where $v$ is the speed of sound in the medium, $u_s$ is the source speed, and $u_o$ is the observer speed (both relative to the medium).
§3 — Doppler Effect for Electromagnetic Waves C.5 SL + HL
For light or any EM wave, when the source–observer relative speed $v$ is much less than $c$ (the non-relativistic limit), the source-vs-observer asymmetry vanishes and a single formula applies:
Redshift & blueshift
| Blueshift | Redshift | |
|---|---|---|
| Relative motion | Approaching | Receding |
| $\Delta\lambda$ | Negative ($\lambda_\text{obs} < \lambda_\text{rest}$) | Positive ($\lambda_\text{obs} > \lambda_\text{rest}$) |
| $\Delta f$ | Positive ($f_\text{obs} > f_\text{rest}$) | Negative ($f_\text{obs} < f_\text{rest}$) |
| Astronomical example | Andromeda galaxy (approaching) | Distant galaxies (Hubble's law) |
§4 — Applications C.5 SL + HL
- Radar speed gun: microwaves reflect off a moving car; the frequency shift $\Delta f = 2 v f / c$ gives the car's speed. The factor of 2 arises because the car acts as both moving observer (on receiving) and moving source (on re-emitting).
- Medical ultrasound: sound reflects off moving blood cells; the frequency shift gives the blood-flow speed. Used in foetal monitoring and cardiology.
- Stellar / galactic motion: spectral line shift gives a star's recession or approach velocity along the line of sight.
- Hubble expansion: all distant galaxies are redshifted, demonstrating that the universe is expanding ($v \approx H_0 d$).
§5 — Exam Attack Plan All sections
When you see this in the question — reach for that:
| Question trigger | Reach for |
|---|---|
| Moving source, find $f'$ | $f' = f \cdot v / (v \mp u_s)$ (subtract for approach). |
| Moving observer, find $f'$ | $f' = f \cdot (v \pm u_o) / v$ (add for approach). |
| Wavelength change for moving source | $\lambda' = (v \mp u_s) / f$. |
| Find observer or source speed from $f, f'$ | Rearrange the appropriate formula. |
| Light from a distant galaxy | $\Delta\lambda/\lambda \approx v/c \Rightarrow v = c\,\Delta\lambda/\lambda$. |
| Redshift or blueshift? | Compare $\lambda_\text{obs}$ and $\lambda_\text{rest}$. |
| Radar speed gun | $\Delta f = 2 v f / c$ (factor of 2!). |
| Medical ultrasound | $\Delta f = 2 v f \cos\theta / c_\text{tissue}$. |
| "Why are spectral lines shifted?" | Source–observer relative motion + Doppler effect. |
| Sanity check | Approaching $\Rightarrow f' > f$; receding $\Rightarrow f' < f$. |
Worked Example — IB-Style HL Doppler Effect Problem
Question (HL Paper 2 style — 7 marks)
A police car siren emits a sound of frequency 750 Hz. The car moves directly towards a stationary observer at 25 m s$^{-1}$. The speed of sound in air is 340 m s$^{-1}$. (a) Calculate the frequency heard by the observer. (b) After passing the observer, the car continues at the same speed. Calculate the new observed frequency. (c) State, with reason, what would change if instead the car were stationary and the observer moved towards it at 25 m s$^{-1}$.
Solution
- Source moving towards observer — use $f' = f \cdot v / (v - u_s)$ with $v = 340$, $u_s = 25$. (M1)
- $f' = 750 \cdot 340 / (340 - 25) = 750 \cdot 340 / 315 = 809.5\ \mathrm{Hz} \approx 810\ \mathrm{Hz}$. (A1)
- After passing, source moving away — use $f' = f \cdot v / (v + u_s)$. $f' = 750 \cdot 340 / 365 = 698.6\ \mathrm{Hz} \approx 699\ \mathrm{Hz}$. (M1)(A1)
- For a moving observer towards a stationary source: $f' = f \cdot (v + u_o) / v = 750 \cdot 365 / 340 = 805.1\ \mathrm{Hz} \approx 805\ \mathrm{Hz}$. (M1)(A1)
- The observed frequency is different (805 Hz vs 810 Hz) even though the relative speed is the same. This is because the source's motion compresses wavefronts in the medium, while a moving observer simply intercepts unchanged wavefronts at a different rate. (R1)
Examiner's note: The most common error is using the wrong formula — putting $u_s$ in the numerator or $u_o$ in the denominator. Always sketch the situation, identify which is moving (source vs observer), and apply the correct formula. The asymmetry (different answers for the same speed) is the conceptual point Topic C.5 is testing.
Common Student Questions
Is the moving-source formula different from the moving-observer formula?
How do I know which sign to use in the Doppler formula?
What is the difference between redshift and blueshift?
Why is there a factor of 2 in the radar speed-gun formula?
When can I use the simple $\Delta f / f = v/c$ formula?
Get the printable PDF version
Same cheatsheet, formatted for A4 print — keep it next to your study desk. Free for signed-in users.