The document discusses the Doppler effect, which is a change in frequency of a wave as the distance between the source and observer changes over time due to their relative motion. It provides examples of how the Doppler effect can be observed with approaching and receding sound sources. The key points are: - The frequency observed is higher when the source is approaching and lower when receding, due to the compression and rarefaction of the waves. - Simple formulas are derived showing the relationship between source frequency, observed frequency, and speed of source and observer. - The Doppler effect can be used to measure speeds, such as blood flow or speed of vehicles, by analyzing the observed frequency shift. - In the

1. Wave
Phenomena
Topic 9.5 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.
Simple Doppler Effect
Clips of various examples of Doppler Effect

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

9. Which gives you the most chocolates?

11. Deriving the formulae (not required)
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.

12. 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 .

13. 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

14. 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 = 1 f
1- (vs / v)

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

16. 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

17. 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

18. Doppler effect for sound with moving observer

19. Doppler shift for SOUND source
Be careful to apply the + or – the correct way.

20. Example of using Doppler to measure speed:
1. measuring blood flow

21. Example of using Doppler to measure speed:
2. measuring speed of vehicle

22. Caught speeding
Take the case of the car and the radar speed trap. The
emitted frequency of the police radar gun is f, the car acts like
a moving observer receiving it at f'. It reflects it back at f',
acting now as a moving source and the police receive it back
shifted once again as f''.
The total change in frequency (f'' - f) is therefore doubled.

23. It can be shown that the relative Doppler shift for electro-
magnetic radiations like light, radio waves etc is given
(approximately) by
where c is the speed of light and v is the relative speed of
source and observer. The speed of a car is being measured by
a police-person using a "radar speed-measuring gun". The
frequency of the transmitted signal is 5GHz. When "mixed" the
transmitted and received signals beat with a frequency of
750Hz. If the speed limit for the road is 110kmh-1, should the
driver be fined or not?
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