## The Doppler Effect

The Doppler effect occurs when a wave source moves relative to some observer. A common example is when a police car puts on its siren. The siren will emit waves of a particular frequency but the frequency heard by any observer will depend on the motion of the siren relative to that observer. If the siren and observer are approaching each other then the observer will experience a higher frequency sound and if siren and observer are receding from each other then the observer will experience a lower frequency sound.

The speed of the sound waves in air is constant, but the relative motion of source and observer means move waves are squeezed into a smaller length for any observer approaching the source, and stretched into a longer length for any observer receding relative to the source.

There are different equations for the Doppler effect for light and sound waves. The equation for sound waves is given and illustrated below.

The frequency of sound heard by the observer is

The frequency of sound heard by the observer is

Doppler Effect for Electromagnetic Radiation

(1). Hereis 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 for (1) ifis a small fraction of the speed of light.then, the actual Doppler shift, given by