You may well have noticed the shift in frequency that occurs when a vehicle sounding a siren moves towards us, draws level with us, then moves past and away from us. When the vehicle is moved towards us, we hear a higher pitched or higher frequency sound and when it moves away we hear a lower pitch or lower frequency sound. The rise or fall in apparent pitch or frequency increases with the speed of the vehicle.
This phenomenon is called the Doppler shift. Any sort of wave may be Doppler shifted by the relative motion of source and observer. We are interested here in the Doppler shift exhibited by Stars and Galaxies and they move towards and away from us. The full equation for the observed frequency
is given by
Here
is the speed of the observer relative to the source, negative if they approach and positive if they recede from each other. We can write an approximate expression this ifis a small fraction – less than about 10% - of the speed of light.
then 
, the actual Doppler shift, given by
The Doppler shift for Stars and Galaxies is typically quoted in terms of the fractional change in wavelength. It is called the redshift, because, since the Universe is expanding the wavelength is increased on average – think of the waves being stretched out between the Earth and the receding Stars/Galaxies – which means that visible light is moved to the long wavelength or red end of the visible spectrum. The redshift is given the symbol z:
z
Ifis small compared to
– less than about 10% - then this equation may be written z