The Doppler Effect

Waves From a Stationary Source

So far within the Physics curriculum, all waves have been discussed as having been emitted from a stationary wave Source, relative to the observer. Waves generated from this source will propagate in a series of concentric circles (like ripples on a pond), as shown in the diagram below:-

From previous work (Wave Equations), the speed of this propagation can be found using the following formula:-

where :-

V = Wave Speed (ms-1)

f = Wave Frequency (Hz)

λ = Wavelength (m)


Waves From a Moving Source

However, for a moving source, the propagation of waves is very different. The relative motion of the source causes the wave pattern to be distorted, at some points the wave becomes compressed, at other points the wave becomes rarefied. This distortion of the wave pattern due to relative motion is known as the doppler effect.

It is this process that causes the change in pitch on the sound of an ambulance as it approaches you, then moves away again.

Note - The change in pitch is only noticeable to a person moving relative to the sound source. To the paramedics on board the ambulance, the pitch does not change.

The video below shows a summary of the Doppler Effect:-

Breaking the Sound Barrier - Case Study

The distortion caused by relative motion will continue to increase until the source of the wave is travelling with a Velocity equal to the wave speed. At this point, any sound emitted in the direction of motion will be moving with same Velocity and in the same direction as the wave source. This causes the waves to superimpose (effectively "pile up" on top of each other) creating a high intensity shock wave called a sonic boom. The intensity of the shock wave can cause damage on the ground, with windows being smashed or plasterwork on buildings being damaged.

The video below shows the effect of supersonic jet breaking the Sound Barrier.

Note - The cloud that forms around the Jet as it passes the speed of sound is due to the pressure change caused by the shock wave. The change in pressure reduces the temperature of the air, causing water vapour to condense and form a cloud.

Breaking the Sound Barrier - Physics Explanation

The images below show how increasing relative motion distorts the waves emitted by a Source :-

The Animation above shows the propagation of waves around a stationary sound source. The waves are emitted in concentric circles, from a fixed central location.

Diagram 1 above shows the propagation of waves around a moving sound source with a relative Velocity less than the speed of sound. The emitted waves follow the Doppler Effect, with the waves either being compressed or rarefied, depending on the relative motion.

Note - Each wave is still emitted in a concentric circle, the compression and rarefaction of the wave is caused by the moving position of source of the wave.

Diagram 2 above shows the propagation of waves around a moving sound source travelling at exactly the speed of sound. The waves are emitted in the opposite direction to motion continue to be rarefied following the Doppler Effect. Due to the sound source moving at the wave speed, all sound waves emitted in the direction the source is moving are superimposed causing a build up of sound Energy, as can be seen by the overlapping wavefronts in the diagram.


Doppler Calculations

When an ambulance approaches your location, more sound waves every second reach your location, giving an increased Frequency (higher pitched note).

When an ambulance moves away from your location, fewer sound waves every second reach your location, giving a decreased Frequency (lower pitched note).

The formula below allows the apparent Frequency of a wave to be calculated:-

where :-

f0 = Frequency detected by observer (Hz)

fs = Frequency emitted by the source (Hz)

v = Velocity of the sound waves (ms-1)

vs = Relative Velocity to the source (ms-1)

Note - In the above formula there is a choice to be made, due to the presence of ± symbol. The following applies to all calculations of Doppler Effect :-

+ Symbol - Used when source is moving away from observer (f decreases).

- Symbol - Used when source is moving towards the observer (f increases).

Example 1 -

A police car emits sound waves from its siren with a Frequency of 912 Hz. If the police car is travelling at 25 ms-1, calculate:-

1. The maximum Frequency heard by a stationary observer and when it occurred.

2. The minimum Frequency heard by a stationary observer and when it occurred.


f0 = ?

fs = 912 Hz

v = 340 ms-1

vs = 25 ms-1


Maximum - Occurs when police car is moving towards the observer.

f0 = 912 (340 / (340 - 25))

f0 = 984 Hz


Minimum - Occurs when police car is moving away from the observer.

f0 = 912 (340 / (340 + 25))

f0 = 850 Hz

The video below shows a description of the Doppler Effect by Sheldon Cooper :-

Note - Even Dr Cooper can get things wrong from time to time. The visual representation that makes up his costume is wrong from a Physics point of view. Sheldon's costume shows the same amount of compression on both sides of the object. This is incorrect, one side should show the wave rarefied (spread out - longer Wavelength), the other side should show the wave compressed (closer together - shorter Wavelength).