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Wave Phenomena

Wave Phenomena. Topic 11.2 Doppler Effect. 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.

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Wave Phenomena

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  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 = 1 f 1- (vs / v)

  12. If the source was moving away from the observer then we have • f1 = 1 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

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