Activity 8
The Doppler Effect
Background Information
There are numerous examples of the Doppler Effect. Anyone who has watched an auto race has heard the distinctive drop in pitch as a car goes by the microphone.
The same effect can be heard while riding on a train and passing a crossing signal—the pitch of the ding-ding-ding drops distinctly as the train passes the crossing. Remember that when the pitch we hear decreases, that means the frequency of the sound wave decreased too. Notice that in the race car example, the sound source is moving, whereas in the train example, the observer is moving. The physics is perfectly symmetrical.
It is easy to derive an equation for the amount of the shift. Suppose a sound source produces circular waves, as shown in the drawing, with wavelength l. The source begins to move to the right. For waves to the right of the source, the source is moving in the same direction as the wavefronts, so the wavelength in this direction is decreased. Let S be the speed of sound. Since f 5 S/l, decreasing the wavelength increases the frequency.
To find out how much the frequency increases, we simply calculate the observed wavelength, which is reduced by the distance the source travels during one cycle of the wave. One cycle of the wave takes a wave period T, which is the inverse of the frequency f. In this time, the source has moved a distance VxT, where V is the source speed.
λ is simply the “at-rest” wavelength λ0 minus V X T:
λ = λ0 - VT
Doppler-shift measurements on the light from distant galaxies led to one of the most important discoveries in the history of astronomy—the recession of the galaxies. Astronomers identify the spectral lines of certain elements, such as hydrogen, in the light from galaxies. These lines have the same spacing as laboratory measurements on Earth, but all the lines are shifted to longer wavelengths, toward the red end of the spectrum. A longer wavelength means a lower frequency, so these galaxies are receding from Earth. When the distance to these galaxies is measured independently, a pattern emerges: the more distant the galaxy, the faster the galaxy is moving away. This “recession of the galaxies” is an important part of the evidence for the Big Bang Theory. Incidentally, Einstein developed an equation in his Theory of General Relativity (his theory of gravity) that predicted the expansion of the universe. But since he believed
the universe to be static, he introduced an extra term into his equation that made his result come out the way he wanted. Unfortunately, he missed a stunning prediction.
The Doppler Effect
Background Information
There are numerous examples of the Doppler Effect. Anyone who has watched an auto race has heard the distinctive drop in pitch as a car goes by the microphone.
The same effect can be heard while riding on a train and passing a crossing signal—the pitch of the ding-ding-ding drops distinctly as the train passes the crossing. Remember that when the pitch we hear decreases, that means the frequency of the sound wave decreased too. Notice that in the race car example, the sound source is moving, whereas in the train example, the observer is moving. The physics is perfectly symmetrical.
It is easy to derive an equation for the amount of the shift. Suppose a sound source produces circular waves, as shown in the drawing, with wavelength l. The source begins to move to the right. For waves to the right of the source, the source is moving in the same direction as the wavefronts, so the wavelength in this direction is decreased. Let S be the speed of sound. Since f 5 S/l, decreasing the wavelength increases the frequency.
To find out how much the frequency increases, we simply calculate the observed wavelength, which is reduced by the distance the source travels during one cycle of the wave. One cycle of the wave takes a wave period T, which is the inverse of the frequency f. In this time, the source has moved a distance VxT, where V is the source speed. λ is simply the “at-rest” wavelength λ0 minus V X T:
λ = λ0 - VT
The observed frequency is f. Converting to frequency, using λ = S/f and T = 1/f, gives
Solving for f, the observed frequency,
Doppler-shift measurements on the light from distant galaxies led to one of the most important discoveries in the history of astronomy—the recession of the galaxies. Astronomers identify the spectral lines of certain elements, such as hydrogen, in the light from galaxies. These lines have the same spacing as laboratory measurements on Earth, but all the lines are shifted to longer wavelengths, toward the red end of the spectrum. A longer wavelength means a lower frequency, so these galaxies are receding from Earth. When the distance to these galaxies is measured independently, a pattern emerges: the more distant the galaxy, the faster the galaxy is moving away. This “recession of the galaxies” is an important part of the evidence for the Big Bang Theory. Incidentally, Einstein developed an equation in his Theory of General Relativity (his theory of gravity) that predicted the expansion of the universe. But since he believed
the universe to be static, he introduced an extra term into his equation that made his result come out the way he wanted. Unfortunately, he missed a stunning prediction.