Sound travels at about 600 miles per hour. If the sound source is ALSO moving then the sound waves reach you SLIGHTLY faster when the siren is approaching... and slightly slower when the siren passes you by. By the way... Lightwaves do the same thing but you see a shift in the COLOR of the object. That is why some stars have a REDDISH color which can be seen if you live outside the city (where the stars appear brighter)... and have good eyesight. Some stars are moving towards us... some moving away at great speeds.
With lightwaves... it is called REDSHIFT.
With soundwaves... it is called Doppler effect as MAVEN says.