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Doppler Shift

The Doppler effect is the change in frequency of a wave for an observer moving relative to its source. It is most commonly observed in everyday life by the sounding of a siren or horn that approaches, passes and goes away from an observer. The received frequency is higher, compared to the emitted frequency during the approach, is identical at the instant of passing and is low during the recession.

The relative change in frequency can be explained by the source of the wave changing positions. When the waves are travelling, the distance between successive wave fronts is reduced so that waves are “bunched together”. Conversely, if the source of waves is moving away from the observer, each wave is emitted further from the previous. The distance between successive wave fronts is increased and “spread out”.
In classical physics, the speed of the source and the receiver relative to the medium are lower than the velocity of waves in the medium. The observed frequency has a relationship to the emitted frequency given by:

f=( (c+ v_r)/(c+v_s ))f_0

Where c is the velocity of waves in the medium, vr is the velocity of the receiver relative to the medium and vs is the velocity of the source relative to the medium. The change of frequency can be found from the equation:

∆f= ∆v/c f_0

Where

∆f=f- f_0

∆v= v_r- v_s

If the moving source is emitting waves with an actual frequency f0, then an observer stationary relative to the medium detects waves with a frequency f given by:

f=(c/(c+ v_s )) f_0

A similar analysis for a mover observer and a stationary source has the observed frequency:

f=((c+ v_r)/c) f_0

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