The Doppler effect describes the phenomenon that occurs when the source of a wave and the observer of a wave are in motion relative to each other. If the net effect is that the objects are moving closer, the frequency appears to be higher; if the net motion is away from each other, the apparent frequency is lower. In the special case of sound waves where the motion occurs along a line joining the objects,
where is the speed of sound in the medium, is the speed of the observer relative to the medium, and is the speed of the source. Since the apparent frequency is higher when the objects are in motion toward each other, the upper sign, which makes the value of n higher, is used when the relative motion is toward each other, and the lower sign is used when the relative motion is away from each other.
The Doppler effect is also apparent in light. When observing distant celestial objects, those that have net motion toward the Earth appear to be more blue, or blue-shifted, while those with net motion away from the Earth appear to be more red, or red-shifted. This observation is based on the phenomenon that light from objects
