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IBO Diploma Physics Topic 11.2

IBO Diploma Physics Topic 11.2

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11.2 2013 Presentation Transcript

  • 1. WavePhenomena 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.• 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
  • 8. Which gives you the mostchocolates?
  • 9. 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.
  • 10. • 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 .
  • 11. • 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
  • 12. • If f1 is the new frequency, then• 1 = v/ f1 = (v- v ) / f s• Rearranging• f1 = v / (v- vs) * f• Dividing throughout by v gives• f1 = 1 f 1- (vs / v)
  • 13. • If the source was moving away from the observer then we have• f1 = 1 f 1+ (vs / v)
  • 14. 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
  • 15. • 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
  • 16. Doppler effect for sound Hyperlink
  • 17. Doppler effect for sound with moving observer
  • 18. Doppler shift for SOUND source Be careful to apply the + or – the correct way.
  • 19. Doppler sound problems
  • 20. Answers
  • 21. Solve problems on the Doppler effectfor electromagnetic waves using theapproximation Students should appreciate that the approximation may be used only when v << c.
  • 22. Caught by the fuzz. 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. Question 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?
  • 24. Example of using Doppler to measurespeed:1. measuring blood flow
  • 25. Example of using Doppler to measurespeed:2. measuring speed of vehicle