Doppler effect (A-level only) — AQA A-Level Physics

The Doppler effect describes how the observed frequency of a wave changes when there is relative motion between the source and the observer. It applies to all waves, including sound, light, and water waves. In AQA A-Level Physics, you must be able to derive and use the equations for a moving source and a moving observer, and explain the effect in terms of wavefronts.

This topic is crucial for understanding redshift in astronomy, which provides evidence for the Big Bang and an expanding universe. It also has practical applications such as speed guns, medical ultrasound, and radar. Mastering the Doppler effect requires careful attention to sign conventions and the distinction between wave speed, frequency, and wavelength.

• →The observed frequency f' increases when the source and observer move towards each other, and decreases when they move apart.
• →For a stationary observer and a source moving towards them: f' = fv / (v - vs). For a source moving away: f' = fv / (v + vs).
• →For a stationary source and an observer moving towards it: f' = f(v + vo) / v. For an observer moving away: f' = f(v - vo) / v.
• →The wave speed v is determined by the medium and does not change due to relative motion; only frequency and wavelength change.
• →Redshift z = (lambda_obs - lambda_rest) / lambda_rest = delta_lambda / lambda, and for small z, recessional velocity v = cz. Hubble's law v = H0 d links velocity to distance.

• A galaxy is a gravitationally bound system containing stars, gas, dust and dark matter; the Milky Way is the galaxy containing the Solar System.
• A quasar is an extremely luminous active galactic nucleus powered by accretion onto a supermassive black hole, often outshining its host galaxy.
• Spectral lines from galaxies and quasars are compared with laboratory reference wavelengths to identify redshift or blueshift.
• For speeds much less than c, the Doppler shift is approximated by Δλ/λ₀ = v/c, where Δλ is the observed minus rest wavelength and λ₀ is the rest wavelength.
• Large redshifts of quasars indicate high recession speeds and great distances, so they are observed as they were when the universe was younger.
• Quasars are not simply distant galaxies; they are compact, exceptionally luminous active nuclei, whereas galaxies are extended systems of stars and gas.

• 💡When comparing spectra, state clearly whether lines are shifted to longer or shorter wavelengths and link this to motion away from or towards the observer.
• 💡Show the substitution into Δλ/λ₀ = v/c, including the rest wavelength λ₀, before calculating the speed.
• 💡Use the term active galactic nucleus when explaining quasar energy sources, and avoid saying that a quasar is simply a bright star.
• 💡If a question asks why quasars are useful, refer to their extreme luminosity allowing them to be observed at large distances and their large redshifts indicating early cosmic times.
• 💡Always write down the formula you are using and define each symbol. This secures method marks even if arithmetic slips.
• 💡For 'explain' questions, refer to wavefronts: when the source moves towards the observer, wavefronts are compressed, so the wavelength is shorter and frequency higher.
• 💡In redshift calculations, use the rest wavelength as the denominator and state that z is dimensionless. For high speeds, use the relativistic formula if given, but AQA typically uses v = cz for z << 1.

• Treating a quasar as just a very distant galaxy: correct by stating that a quasar is an active galactic nucleus powered by a supermassive black hole and can outshine its host galaxy.
• Using the relativistic Doppler formula when the non-relativistic approximation Δλ/λ₀ = v/c is intended: correct by checking that the recession speed is much less than c before using the simple formula.
• Confusing redshift with blueshift: correct by remembering that redshift means observed wavelengths are longer than rest wavelengths, which corresponds to recession.
• Forgetting to convert wavelength units consistently: correct by converting all wavelengths to the same unit, such as nanometres or metres, before calculating Δλ/λ₀.
• Students think the speed of the wave changes when the source moves. Correction: The wave speed is constant in a given medium; only the observed frequency and wavelength change.
• Students mix up the signs in the Doppler formula. Correction: Always determine whether the source or observer is moving towards or away, and use the formula that increases frequency for approach and decreases for recession.
• Students believe redshift means the galaxy is actually red. Correction: Redshift refers to the increase in wavelength of any electromagnetic radiation due to relative motion away from the observer; it is not about colour.

1. 1Day 1: Revise wave basics and the wave equation. Watch a video on the Doppler effect to visualise wavefront compression.
2. 2Day 2: Learn the two Doppler formulas for moving source and moving observer. Practice 5 calculations for each, paying attention to signs.
3. 3Day 3: Study redshift and Hubble's law. Derive z = delta_lambda / lambda and v = cz. Practice 3 redshift problems.
4. 4Day 4: Attempt exam-style questions on the Doppler effect, including 6-mark explanations. Mark your answers using the mark scheme.
5. 5Day 5: Review common misconceptions and create a summary sheet with key formulas and definitions. Test yourself with active recall prompts.

• 📋Calculation of observed frequency for a moving source or observer. Advice: Identify the correct formula, substitute values, and give units.
• 📋Explanation of the Doppler effect in terms of wavefronts. Advice: Use clear diagrams and refer to compression and stretching of wavefronts.
• 📋Redshift calculation and estimation of distance using Hubble's law. Advice: Calculate z first, then v = cz, then d = v / H0. Keep units consistent.
• 📋Practical application question, e.g., speed gun or ultrasound. Advice: Link the observed frequency shift to the relative speed and use the appropriate formula.