# Doppler effect

The Doppler effect is the apparent change in frequency or wavelength of a wave emitted by a moving body and received by a stationary observer.

Christian Andreas Doppler first postulated the Doppler effect in 1845 by standing next to a rail line and listening to a car full of muscians as they approached him and after they passed him. The pitch is higher as the sound source approaches and lower as the sound source moves away from you.

It is important to realize that the frequency of the sounds that the source emits does not actually change. To understand what happens, consider the following analogy. Someone throws one ball every second in your direction. Assume that balls travel with constant velocity. If the thrower is stationary, you will receive one ball every second. However, if he is moving towards you, you will receive more than that because there will be less spacing between the balls. The converse is true if the person is moving away from you. So it is actually the wavelength which is affected; as a consequence, the perceived frequency is also affected.

If the moving source is emitting waves (e.g. sound waves) with an actual frequency f0, a stationary observer detects waves with a frequency f given by:

f = f0 v / (v - vs) ,

(where v is the speed of the waves in the medium and vs is the speed of the source with respect to the observer (positive if moving towards the observer, negative if moving away).

The Doppler effect is not quantitatively the same depending on whether the theory of relativity is taken into account. See relativistic Doppler effect.

### Applications

The Doppler effect has been of great use to astronomy. It has been used to measure the speed of stars moving away from us and hence the age of the universe (see redshift). The spectrum from the stars is not continuous - there are well defined gaps in the spectrum which correlate to the energies required to excite electrons in various elements from one level to another. These absorption lines are not always in exactly the same place; for most stars these are shifted towards the red (longer wavelength) end of the spectrum by a small amount, although a few do have blueshifts. These shifts are generated in exactly the same way as the shifts in wavelength and frequencies for sound. The fact that the more distant objects have a redshift proportional to their distance is evidence for an expanding universe, and is the Hubble Constant, Ho, the inverse of the age of the universe, equal to the speed of recession divided by the distance. Current values for the Hubble constant are between ten and twenty billion years.

The Doppler effect is also used in some forms of radar to measure the velocity of detected objects. A radar beam is fired at a moving target - a car, for example, as radar is often used by police to detect speeding motorists - as it receeds from the radar source. Each successive wave has to travel further to reach the car, before being reflected and re-detected near the source. As each wave has to move further, the gap between each wave increases, increasing the wavelength.