11.2

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11.2

  1. 1. Wave Phenomena Topic 11.2 Doppler Effect
  2. 2. The Doppler Effect <ul><li>This effect is the change in the frequency of a wave received by an observer, compared to the frequency with which it was emitted. </li></ul><ul><li>The effect takes place whenever there is motion between the emitter and receiver. </li></ul>
  3. 3. <ul><li>This is a phenomenon of everyday life. </li></ul><ul><li>On a highway, an approaching car creates a high pitched sound. </li></ul><ul><li>As it goes past us and recedes from us the frequency becomes lower. </li></ul>
  4. 4. <ul><li>In diagrams we can explain the Doppler effect as follows: </li></ul>
  5. 5. <ul><li>This diagram can be constructed accurately to show the pattern </li></ul><ul><li>As can the pattern for a moving detector. </li></ul>
  6. 6. <ul><li>T he source moves towards observer B and away from observer A. </li></ul><ul><li>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. </li></ul><ul><li>Thus the received period is smaller and hence the frequency is larger. </li></ul><ul><li>On the other hand, the crests reach A at longer time intervals and thus the measured frequency is smaller . </li></ul>
  7. 7. <ul><li>The frequency of the sound emitted from the stationary source is f </li></ul><ul><li>Observer A will hear a note of frequency f A where f A  f </li></ul><ul><li>Observer B will hear a note of frequency f B where f B  f </li></ul><ul><li>This shift in frequency is known as the Doppler effect </li></ul>
  8. 8. Deriving the formulae <ul><li>Let us look at the simplest case in which the velocity of the source is in line with the observer </li></ul><ul><li>In the diagram the observer 0 is at rest with respect to the medium and the source is moving with speed v s . </li></ul>
  9. 9. <ul><li>The source is emitting a note of constant frequency f that travels with speed v in the medium. </li></ul><ul><li>S' shows the position of the source  t later. </li></ul><ul><li>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 . </li></ul>
  10. 10. <ul><li>The wavelength = distance occupied by the waves  the number of waves </li></ul><ul><li>The wavelength = v  t / f  t = v/f </li></ul><ul><li>Because of the motion of the source this number of waves will now occupy a distance v  t - v s  t </li></ul><ul><li>The ´new´wavelength = (v  t - v s  t ) / f  t </li></ul><ul><li>i.e.  1 = (v- v s ) / f </li></ul>
  11. 11. <ul><li>If f 1 is the new frequency, then </li></ul><ul><li> 1 = v/ f 1 = (v- v s ) / f </li></ul><ul><li>Rearranging </li></ul><ul><li>f 1 = v / (v- v s ) * f </li></ul><ul><li>Dividing throughout by v gives </li></ul><ul><li>f 1 = 1 f </li></ul><ul><li>1- (v s / v) </li></ul>
  12. 12. <ul><li>If the source was moving away from the observer then we have </li></ul><ul><li>f 1 = 1 f </li></ul><ul><li>1+ (v s / v) </li></ul>
  13. 13. And for moving observer <ul><li>Observer moving towards source </li></ul><ul><li>Relative velocity = v +v O </li></ul><ul><li>f 1 = (V + V O )/  </li></ul><ul><li>But  = v/f </li></ul><ul><li>Therefore f 1 = (V + V O )/ v/f </li></ul><ul><li>Rearranging gives </li></ul><ul><li>f 1 = ((V + V O )/ v )f </li></ul>
  14. 14. <ul><li>If the observer is moving towards the source </li></ul><ul><li>f 1 = (1+ (v O / v)) f </li></ul><ul><li>If the observer is moving away from the source </li></ul><ul><li>f 1 = (1- (v O / v)) f </li></ul>

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