Doppler Race Car
Neee-owww! Why does a car's horn sound higher as it comes towards you and lower as it drives away? Watch the sound waves and listen.
- Horn plays
- 400 Hz
- You hear
- 452 Hz
- Coming towards you
- 453 Hz
- Going away
- 358 Hz
The maths, live
Coming towards you f′ = f × v ÷ (v − vs)f′ = 400 × 343 ÷ (343 − 40) = 453 HzGoing away f′ = f × v ÷ (v + vs)f′ = 400 × 343 ÷ (343 + 40) = 358 HzRight now f′ = f × v ÷ (v − vs × cos θ)f′ = 400 × 343 ÷ (343 − 40 × 0.99) = 452 HzTurn the sound on and listen as the car passes: high, then a quick swoop down. The faster the car, the bigger the swoop.
How it works
The horn sends out waves at a steady rate, but the car keeps moving. In front of the car each new wave starts a little closer to the last one, so the waves bunch up and you hear a higher pitch. Behind the car they spread out, so the pitch is lower. This is the Doppler effect.
Coming straight towards you, the frequency you hear is f′ = f × v ÷ (v − vs), where v = 343 m/s is the speed of sound and vs is the car's speed. Going away it is f′ = f × v ÷ (v + vs). The horn itself never changes: only the waves reaching your ear do.
Try this
- Set the car to 30 m/s. How much higher does the horn sound as it comes towards you?
- Make the car twice as fast. Is the change in pitch twice as big?
- Watch the wave fronts. Where are they closest together?