Short on time? This page is the recap. For the wavefront diagram and the worked examples, use the full study guide.
Recap
- Rest frequency f₀: how often the source vibrates. An observer moving with the source measures f₀.
- Observed frequency f: how many wavefronts reach a given observer each second.
- Doppler effect: f differs from f₀ because of the relative velocity of source and observer.
- Travel-time argument: if the distance between source and observer is shrinking, each crest has a shorter trip than the last, so crests arrive closer together in time (f > f₀). Growing distance gives f < f₀. Constant distance gives f = f₀.
- Moving source in a medium: wavefronts bunch up ahead (shorter λ) and spread out behind (longer λ). The wave speed is set by the medium and does not change.
- Moving observer: the wavelength in the medium is unchanged, but the observer meets crests more often (approaching) or less often (receding).
- Light: no medium is needed; only relative velocity matters.
- In this course the Doppler effect is qualitative: predict, compare and justify. No Doppler formula is needed.
Key relationships
| Situation | Observed frequency | Observed wavelength (sound ahead/behind a source, or light) |
|---|---|---|
| Separation shrinking (approaching) | f > f₀ | shorter |
| Separation growing (receding) | f < f₀ | longer |
| Separation constant (same velocity, or motion across the line of sight) | f = f₀ | unchanged |
| Larger relative speed along the line | larger |f − f₀| | larger change |
| Passing source at constant speed | What you hear |
|---|---|
| Approaching | steady pitch above f₀, getting louder |
| Passing | pitch falls quickly through f₀ |
| Receding | steady pitch below f₀, getting quieter |
Assumptions behind the rules
- Speeds are constant unless the question says otherwise.
- For sound, the medium (air) is still, or any wind is steady.
- Speeds of sources are well below the wave speed.
Mistakes to avoid
- Saying the source’s own frequency changes. It does not.
- Rising pitch on approach. At constant velocity the pitch is constant while approaching.
- Mixing up pitch and loudness. Pitch ↔ frequency; loudness ↔ amplitude.
- Changing the wave speed. Source motion changes λ in the medium, not v.
- Red shift = approaching. Red shift means receding (longer λ).
Quick self-check
- A drone hovers beside you and beeps. Then it flies away from you at constant speed. What happens to the pitch you hear? (It drops below f₀ and stays at that lower value while the drone recedes at constant speed.)
- Two cyclists ride side by side at the same velocity; one rings a bell. Does the other hear a shift? (No: their separation is constant.)
- Wavefronts ahead of a moving source in air are 0.50 m apart and sound travels at 340 m/s. What frequency reaches a still observer there? (680 Hz, from v = fλ.)
- A spectral line from a galaxy is measured at a shorter wavelength than in the laboratory. What does that show? (The galaxy is approaching: blue shift.)
Next: practice questions.