Properties of Waves » The Doppler Effect

A sound that changes as it passes

Stand by a road as an ambulance races past with its siren on. As it comes towards you the siren sounds high. As it passes, the note drops, and it stays lower as the ambulance drives away. The same thing happens at a motor racing track. A passing racing car makes a sound like 'neeee-yooow': high as it comes towards you, low as it goes away.

The siren and the engine have not changed. The paramedic inside the ambulance hears the same steady note all the time. What has changed is the sound that reaches you, because the thing making the sound is moving.

The spec puts it like this: there is a change in the observed frequency and wavelength of a wave when its source is moving relative to an observer. This is known as the Doppler effect.

Key terms:

• Source: the object that makes the waves, such as a siren.
• Observer: the person or instrument that receives the waves.
• Observed frequency: the frequency of the waves that the observer receives. It can be different from the frequency the source gives out.
• Doppler effect: the change in the observed frequency and wavelength of a wave when its source is moving relative to an observer.

Start with a source that is not moving

Picture a siren standing still, seen from above. Remember, a wavefront is a line joining points on a wave that are at the same stage of the vibration. The siren sends out wavefronts that spread out in every direction, like the rings that spread out when a raindrop lands in a puddle.

To draw this, mark a dot for the source. Then draw four or five circles around it, all with the dot at their centre, with equal gaps between them. The gap between one circle and the next is one wavelength. The gaps are the same on every side, so an observer standing anywhere receives the same wavelength and the same frequency.

Now the source moves

Suppose the siren moves steadily to the right. It still sends out wavefronts at the same rate. Each wavefront still spreads out as a circle from the place where it was made. But the siren has moved a little to the right before it sends out the next one. So each new circle starts from a point further to the right than the one before.

To draw this, mark four dots in a row, close together, for four positions of the source. Draw the biggest circle around the left-hand dot, because that wavefront was sent out first and has had the longest time to spread. Draw a smaller circle around the next dot, and so on, with the smallest circle around the right-hand dot. The circles no longer share a centre. On the right they are squashed close together. On the left they are spread far apart.

	Source moving towards the observer	Source moving away from the observer
Wavefronts	bunch up (closer together)	spread out (further apart)
Observed wavelength	shorter	longer
Observed frequency	higher	lower
Wave speed	no change	no change

The wave speed does not change

This is the part many students miss. Once a wavefront has left the source, it travels through the air at the speed of sound in air. That speed is set by the air, not by how fast the source is moving. A fast ambulance does not throw its sound forwards any faster.

Now use the equation from The Wave Equation, v = f × λ. The wave speed v stays the same. In front of the source the wavelength λ is shorter, so the frequency f must be higher. Behind the source the wavelength is longer, so the frequency must be lower.

A higher frequency sound is heard as a higher note. That is why the siren sounds higher as it comes towards you and lower as it goes away. (You will meet this link properly in Oscilloscopes, Pitch and Loudness.)

Explaining it step by step

The spec says 'explain' for this topic, so learn this chain for a source moving towards an observer:

1. The source moves towards the observer while it gives out waves.
2. Each wavefront is sent out from a point closer to the observer than the one before.
3. So the wavefronts in front of the source bunch up, and the observed wavelength is shorter.
4. The wave speed does not change.
5. So the wavefronts reach the observer more often: the observed frequency is higher.

For a source moving away, turn each step round: each wavefront is sent out from further away, the wavefronts spread out, the wavelength is longer, the speed is the same, and the observed frequency is lower.

'Relative to an observer'

The effect only happens when the distance between the source and the observer is changing. The paramedic travels along with the siren, so the siren is not moving relative to the paramedic. The paramedic hears the true frequency. You, at the side of the road, do not.

Speed matters too. The faster the source moves, the more the wavefronts bunch up in front and spread out behind, so the bigger the change in frequency. That is why the drop in note from a racing car is much more obvious than the drop from a passing bicycle bell.

It happens for all waves

The Doppler effect is not just about sound. It happens for every kind of wave. A duck paddling across a pond makes ripples that are close together in front of it and far apart behind it. It happens for light too: light from a source that is moving away from us is observed with a longer wavelength and a lower frequency. You will use this idea in Red-shift of Light from Galaxies.

Exam-style question

A train sounds its horn as it travels at a steady speed along a straight track. A man stands still on a station platform. The train moves towards him, passes him and then moves away.

(a) State the name of the effect that changes the sound the man hears. [1 mark]

(b) Explain why the frequency of the sound the man hears is higher than the frequency given out by the horn while the train is moving towards him. [4 marks]

(c) Describe how the wavelength and the frequency of the sound the man hears change when the train has passed him and is moving away. [2 marks]

(d) State how the speed of the sound waves in the air when the train is moving compares with their speed when the train is standing still. [1 mark]

(e) The train driver hears the horn at the same frequency all the time. Suggest why. [1 mark]