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11.2

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Transcript

  • 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.
    • T he 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 f A where f A  f
    • Observer B will hear a note of frequency f B where f B  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 v s .
  • 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 - v s  t
    • The ´new´wavelength = (v  t - v s  t ) / f  t
    • i.e.  1 = (v- v s ) / f
  • 11.
    • If f 1 is the new frequency, then
    •  1 = v/ f 1 = (v- v s ) / f
    • Rearranging
    • f 1 = v / (v- v s ) * f
    • Dividing throughout by v gives
    • f 1 = 1 f
    • 1- (v s / v)
  • 12.
    • If the source was moving away from the observer then we have
    • f 1 = 1 f
    • 1+ (v s / v)
  • 13. And for moving observer
    • Observer moving towards source
    • Relative velocity = v +v O
    • f 1 = (V + V O )/ 
    • But  = v/f
    • Therefore f 1 = (V + V O )/ v/f
    • Rearranging gives
    • f 1 = ((V + V O )/ v )f
  • 14.
    • If the observer is moving towards the source
    • f 1 = (1+ (v O / v)) f
    • If the observer is moving away from the source
    • f 1 = (1- (v O / v)) f