DOPPLER EFFECT
If an observer is moving relative to a source of light or the source is moving relative to him, then the observer will see a change in the wavelength of the light:
DOPPLER PRINCIPLE: Electromagnetic radiation received by an observer will have a shorter wavelength if source and observer approach each other and a longer wavelength if they recede from each other; the amount of change in wavelength is directly proportional to the velocity along the line between source and observer.
To see why, suppose a stationary light source is radiating concentric waves of one wavelength in all directions. Then observers in any direction, if stationary, would see successive crests of the wave passing them at the same rate at which they were emitted by the source. If, on the other hand, the light source begins to move at uniform speed toward the right, the two observers 0 and P along the line of motion would see crests passing them at rates different from that with which they were emitted. Observers Q and R, located at right angles to the moving source, would detect no change in the rate for crests passing them. Observers elsewhere would notice some change, the amount depending on the angle between their radial direction to the source and the line of motion. This phenomenon is known as the Doppler effect, named for Christian Doppler (18031853), the Austrian physicist who first explained it.
Let us consider observers 0 and P in more detail. Wave 1 was produced when the light source was at position 1; wave 2, when it was at position 2i and so on. Because of the greater distance the wave travels in reaching observer 0, each successive wave crest passes him at a slower rate (lower frequency) than when the source was stationary. Because the waves travel a shorter distance to reach P, the successive crests pass at a faster rate (higher frequency). The wavelength is shifted toward longer wavelengths (red shifted) as the source recedes from 0 and toward shorter wavelengths (blue shifted) as the source approaches P.
An example of the Doppler effect familiar to all of us is the change in frequency of sound waves in the rising and falling pitch of a train whistle as the train approaches and then moves away. It is immaterial whether the light source is in motion, or the observer, or both: The size of the Doppler effect seen for light waves depends only on the net relative motion along the line of sight between the light source and the observer.
The amount of the wavelength shift due to the Doppler effect is directly proportional to the velocity of approach (blue shift) or recession (red shift) as long as the relative velocity is well below the velocity of light. (Later in this book we discuss the relationship when the relative velocity is a substantial fraction of the velocity of light.) The constant of proportionality is the rat,io of undisplaced wavelength to the velocity of light. This means that the wavelength shift is greater the longer the wavelength of the radiation.
As an example, if we are approaching two stationary radiation sources, with one emitting electromagnetic radiation twice the wavelength of the other, then we should expect twice the wavelength shift from that one. I n the nearby box we present the mathematical form of the Doppler effect. Because of the continual movement of all bodies in the cosmos, the Doppler effect is an important tool for detecting and measuring the amount of motion.
