Preview
The Doppler Effect
IB DP Physics — Unit C: Wave Behaviour | SL & HL | C.5 Doppler Effect
📋 What You Will Learn
- Observe and describe the Doppler effect using real-world examples involving sound and light
- Define all key quantities — observed frequency, source frequency, wave speed, and velocities of source and observer
- Derive the Doppler equation for sound from first principles using wavefront diagrams
- Apply the Doppler equations for both sound and electromagnetic radiation to solve quantitative problems
- Analyse wavefront diagrams to determine whether frequency increases or decreases
- Evaluate common misconceptions and connect the Doppler effect to astrophysics, medicine, and radar technology
🌍 Real-World Context Stand on a pavement as an ambulance rushes past with its siren wailing. Before it reaches you, the siren sounds noticeably higher-pitched than usual. The moment it passes and moves away, the pitch drops — sometimes dramatically. The ambulance driver hears a constant pitch the whole time, yet you hear two completely different sounds. The siren has not changed; the speed of sound in air has not changed; and yet the frequency you detect is different depending on whether the source is approaching or receding. Something about the relative motion between you and the ambulance is altering the number of wave crests that reach your ear each second. Understanding exactly why this happens — and being able to calculate the shift precisely — is the goal of this topic.
🔍 Guiding Question How does the relative motion between a wave source and an observer change the frequency detected, and what does this tell us about the universe we live in?
Physical Setup and Wavefront Diagrams
Imagine a source of sound — a loudspeaker, a siren, or a musical instrument — emitting waves at a constant frequency. When both the source and the observer are stationary, the wavefronts (surfaces of constant phase, such as compressions in a sound wave) spread out as concentric spheres centred on the source. The observer detects the same frequency that the source emits, because the same number of wavefronts arrive per second as are produced per second.
Now suppose the source begins to move toward the observer. As the source moves, it "catches up" with the wavefronts it has already emitted in the forward direction, compressing them closer together. In the backward direction, the source moves away from the wavefronts it emitted earlier, stretching them further apart. The result is that wavefronts are bunched up ahead of the moving source and spread out behind it.
The key insight from this diagram is that the wavelength — the distance between successive wavefronts — is shorter in the direction the source is moving toward, and longer in the direction it is moving away from. Since the speed of sound in the medium is unchanged, a shorter wavelength means more wavefronts arrive per second, which means a higher detected frequency. A longer wavelength means fewer wavefronts per second, which means a lower detected frequency.
Core Concepts and Definitions
Before we can write any equations, we need to be precise about what we mean by "frequency" in this context. There are two frequencies involved in any Doppler situation: the frequency at which the source emits waves, and the frequency at which the observer detects them.