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11.2

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    11.2 11.2 Presentation Transcript

    • 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.
      • 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.
      • In diagrams we can explain the Doppler effect as follows:
      • This diagram can be constructed accurately to show the pattern
      • As can the pattern for a moving detector.
      • 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 .
      • 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
    • 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 .
      • 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 .
      • 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
      • 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)
      • If the source was moving away from the observer then we have
      • f 1 = 1 f
      • 1+ (v s / v)
    • 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
      • 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