1. Wave Phenomena
Topic 11.2 Doppler Effect

2. The Doppler Effect
This effect is the change in the frequency of a wave received by an observer, compared to the frequency with which it was emitted.
The effect takes place whenever there is motion between the emitter and receiver.

3. This is a phenomenon of everyday life.
On a highway, an approaching car creates a high pitched sound.
As it goes past us and recedes from us the frequency becomes lower.

4. In diagrams we can explain the Doppler effect as follows:

5. This diagram can be constructed accurately to show the pattern
As can the pattern for a moving detector.

6. The source moves towards observer B and away from observer A.
The wavecrests are piling in front of the source and thus the crests reach B at time intervals which are shorter than those on emission.
Thus the received period is smaller and hence the frequency is larger.
On the other hand, the crests reach A at longer time intervals and thus the measured frequency is smaller.

7. The frequency of the sound emitted from the stationary source is f
Observer A will hear a note of frequency fA where fA  f
Observer B will hear a note of frequency fB where fB  f
This shift in frequency is known as the Doppler effect

8. Deriving the formulae
Let us look at the simplest case in which the velocity of the source is in line with the observer
In the diagram the observer 0 is at rest with respect to the medium and the source is moving with speed vs.

9. The source is emitting a note of constant frequency f that travels with speed v in the medium.
S' shows the position of the source t later.
In a time t the observer would receive ft waves and when the source is at rest these waves will occupy a distance vt .

10. The wavelength = distance occupied by the waves  the number of waves
The wavelength = vt / ft = v/f
Because of the motion of the source this number of waves will now occupy a distance vt - vst
The ´new´wavelength = (vt - vst) / ft
i.e. 1 = (v- vs) / f

11. If f1 is the new frequency, then
1 = v/ f1 = (v- vs) / f
Rearranging
f1 = v / (v- vs) * f
Dividing throughout by v gives
f1 = f
1- (vs / v)

12. If the source was moving away from the observer then we have
f1 = f
1+ (vs / v)

13. And for moving observer
Observer moving towards source
Relative velocity = v +vO
f1 = (V + VO)/ 
But  = v/f
Therefore f1 = (V + VO)/ v/f
Rearranging gives
f1 = ((V + VO)/ v )f

14. If the observer is moving towards the source
f1 = (1+ (vO / v)) f
If the observer is moving away from the source
f1 = (1- (vO / v)) f