5.6 The doppler effect  (Page 2/35)

The situation is not the same for other observers. Let’s look at the situation from the point of view of observer C , located opposite observer A in the figure. For her, the source is moving away from her location. As a result, the waves are not squeezed together but instead are spread out by the motion of the source. The crests arrive with an increased wavelength and decreased frequency. To observer B , in a direction at right angles to the motion of the source, no effect is observed. The wavelength and frequency remain the same as they were in part (a) of the figure.

We can see from this illustration that the Doppler effect is produced only by a motion toward or away from the observer, a motion called radial velocity    . Sideways motion does not produce such an effect. Observers between A and B would observe some shortening of the light waves for that part of the motion of the source that is along their line of sight. Observers between B and C would observe lengthening of the light waves that are along their line of sight.

You may have heard the Doppler effect with sound waves. When a train whistle or police siren approaches you and then moves away, you will notice a decrease in the pitch (which is how human senses interpret sound wave frequency) of the sound waves. Compared to the waves at rest, they have changed from slightly more frequent when coming toward you, to slightly less frequent when moving away from you.

Color shifts

When the source of waves moves toward you, the wavelength decreases a bit. If the waves involved are visible light, then the colors of the light change slightly. As wavelength decreases, they shift toward the blue end of the spectrum: astronomers call this a blueshift (since the end of the spectrum is really violet, the term should probably be violetshift , but blue is a more common color). When the source moves away from you and the wavelength gets longer, we call the change in colors a redshift . Because the Doppler effect was first used with visible light in astronomy, the terms “ blueshift ” and “ redshift ” became well established. Today, astronomers use these words to describe changes in the wavelengths of radio waves or X-rays as comfortably as they use them to describe changes in visible light.

The greater the motion toward or away from us, the greater the Doppler shift. If the relative motion is entirely along the line of sight, the formula for the Doppler shift of light is

where λ is the wavelength emitted by the source, Δλ is the difference between λ and the wavelength measured by the observer, c is the speed of light, and v is the relative speed of the observer and the source in the line of sight. The variable v is counted as positive if the velocity is one of recession, and negative if it is one of approach. Solving this equation for the velocity, we find v = c × Δλ/λ.