moving away from you. This effect occurs because the motion of the siren changes the
frequency of the sound waves that reach you.
The change in the frequency depends on whether you move toward the source of a
sound, or the source moves toward you. There is an asymmetry because sound travels
through a medium, and it matters which reference frame í yours or the source’s í is
stationary with respect to the medium.
In contrast, light requires no medium. With light (and other electromagnetic radiation),
the Doppler effect depends solely on the relative motion of the source of the light and
the observer of the light. In some ways, this makes the Doppler shift “easier” to
calculate with light.
On the right, we show equations for calculating the change in perceived frequency due
to the Doppler shift. The symbol f 0 represents the frequency of the light as it is emitted
from the source (or as it would be perceived by an observer stationary relative to the
source). This is called the proper frequency. The symbol f represents the frequency
perceived by an observer in a reference frame in which the source is moving at speed
v. The speed is always positive. The two equations are the same except for the signs;
the signs differ for the reasons discussed below.
When the observer and the source are moving toward one other, the frequency of the
light seen by the observer will increase. The speed of the wave í the speed of light í
must remain constant. Since the wavelength equals the speed of light divided by the
frequency, then as the frequency increases, the wavelength decreases. When the
source is moving away from the observer, the opposite effect occurs: The wave
frequency decreases and the wavelength increases.
With light, decreasing wavelength due to the approach of the light source is called a
blue shift since shorter wavelengths occur near the blue end of the visible spectrum.
Increasing wavelength due to the recession of the light source is called a red shift.
Almost all distant stars and galaxies, in whatever direction you look, exhibit red shift. In
fact, the farther away they are, the greater the red shift. This is used as evidence that
the universe is expanding.
The Doppler effect proved to be crucial to astronomers trying to understand the nature
of the universe. Einstein’s work provided grounds for believing that the universe was
expanding, an implication that proved quite troubling to Einstein himself, who
“corrected” his equations to provide for a static universe. But several years after
Einstein performed this correction, the American astronomer Edwin Hubble
(1889í1953) showed that distant stars and galaxies exhibit a red shift.
Astronomers like Hubble were trained to expect certain patterns in the light emanating
from stars. Elements like calcium in the atmospheres of stars absorb certain
wavelengths of light; these show up as “gaps” íspectral linesí in the light emitted from
stars. Hubble expected those spectral lines to occur at certain wavelengths. Instead, he
found them “red shifted” to different wavelengths. Although Hubble knew that the
Doppler shift could account for these changes, he and his colleagues were astonished
that stars in every direction were moving away.
The debate about the nature and fate of the universe continues; but the red shift of
starlight provided crucial data to scientists that caused them to further examine the
possibility that the universe is expanding. The second sample problem to the right
challenges you to compute the speed at which a galaxy is moving away from the Earth
based on the shift in its observed wavelength.
Light source closing in
Blue shift
Light source moving away
Red shift