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18 The Doppler Effect
light can be illustrated in a laboratory. If we heat up a gas of sodium atoms, for
example, the radiating atoms receive an increase in thermal velocity, with which the
atoms alternatively move towards and away from us. If they move towards us, the
frequency of the light we receive increases; if the atoms move away, the frequency
decreases just as with the fire engine. Due to the rapid changing velocities, we cannot
determine the singular changing frequencies, we can only determine the sum of the
changes—as if we had a squadron of fire engines on an airfield moving back and
forth with varying velocities, whose audible signals we register. We therefore register
the sum of all sodium lines displaced to the left or to the right, in other words a thick
line which becomes even thicker the more a gas is heated up.
This is the Doppler effect: An emitter sends out a harmonic wave, in other words,
a sine-shaped oscillation of a certain constant ν o frequency determined by the construction of the emitter. The experimenter, who is resting with respect to this emitter,
therefore measures just this frequency ν o . If however the observer and the emitter
move towards one another, then the observer registers a higher frequency; if both of
them move away from each other, then the observer register a lower frequency.
The Doppler effect occurs independent of the nature of the waves that are sent out
and observed. It is of no difference if the waves are sound waves in water or in air or
even light waves. We can always register the Doppler effect if the emitter and observer
move relatively to one another. Do the same equations apply to all these Doppler
effects? Aren’t sound and light waves something completely different? Doesn’t the
former just cause a mechanical medium to oscillate, and these oscillations then
propagates towards us, whereas we receive light as factual messengers from distant
stars?
Let us begin with the Doppler effect as it was originally discovered by Christian
Doppler in 1842, who has already completely described it. It is remarkable that C.
Doppler originally predicted this effect for light. Not until three years later was this
effect tested in acoustics. (The fast fire engines that today incite us to contemplate
on the change of frequency did not exist in those days). Let us therefore begin with a
description, a description that could have been made in 1842, and a description that
can be found in physics course books today. We will start with the less complicated
acoustic Doppler effect out of grounds of simplicity.
In order to be able to measure something, we need three things. Firstly the source,
let us say, a standard emitter S. This emitter, a tuning fork, is able, due to its construction regulations, to oscillate. Its two arms are able to oscillate 440 times per
second when knocked. We now also need a medium that is also in a position to
oscillate in response to the oscillating arms of the tuning fork. In other words, the
tuning fork excites a wave in the medium, which then moves through the medium
with the characteristic wave velocity for exactly this medium. A medium that can
oscillate with any arbitrary frequency would be the best choice, so that the medium
itself would not be the cause for any frequency distorsions. In Chap. 4, we described
that the mechanical continuum, the limiting case of the linear chain, is just such
a medium. Here, waves of any frequency can propagate dispersion free, in other
words with a velocity independent of frequency, for example with the transversal
sound velocity c T . Our mechanical continuum is therefore ideal for our purposes.
18 The Doppler Effect
light can be illustrated in a laboratory. If we heat up a gas of sodium atoms, for
example, the radiating atoms receive an increase in thermal velocity, with which the
atoms alternatively move towards and away from us. If they move towards us, the
frequency of the light we receive increases; if the atoms move away, the frequency
decreases just as with the fire engine. Due to the rapid changing velocities, we cannot
determine the singular changing frequencies, we can only determine the sum of the
changes—as if we had a squadron of fire engines on an airfield moving back and
forth with varying velocities, whose audible signals we register. We therefore register
the sum of all sodium lines displaced to the left or to the right, in other words a thick
line which becomes even thicker the more a gas is heated up.
This is the Doppler effect: An emitter sends out a harmonic wave, in other words,
a sine-shaped oscillation of a certain constant ν o frequency determined by the construction of the emitter. The experimenter, who is resting with respect to this emitter,
therefore measures just this frequency ν o . If however the observer and the emitter
move towards one another, then the observer registers a higher frequency; if both of
them move away from each other, then the observer register a lower frequency.
The Doppler effect occurs independent of the nature of the waves that are sent out
and observed. It is of no difference if the waves are sound waves in water or in air or
even light waves. We can always register the Doppler effect if the emitter and observer
move relatively to one another. Do the same equations apply to all these Doppler
effects? Aren’t sound and light waves something completely different? Doesn’t the
former just cause a mechanical medium to oscillate, and these oscillations then
propagates towards us, whereas we receive light as factual messengers from distant
stars?
Let us begin with the Doppler effect as it was originally discovered by Christian
Doppler in 1842, who has already completely described it. It is remarkable that C.
Doppler originally predicted this effect for light. Not until three years later was this
effect tested in acoustics. (The fast fire engines that today incite us to contemplate
on the change of frequency did not exist in those days). Let us therefore begin with a
description, a description that could have been made in 1842, and a description that
can be found in physics course books today. We will start with the less complicated
acoustic Doppler effect out of grounds of simplicity.
In order to be able to measure something, we need three things. Firstly the source,
let us say, a standard emitter S. This emitter, a tuning fork, is able, due to its construction regulations, to oscillate. Its two arms are able to oscillate 440 times per
second when knocked. We now also need a medium that is also in a position to
oscillate in response to the oscillating arms of the tuning fork. In other words, the
tuning fork excites a wave in the medium, which then moves through the medium
with the characteristic wave velocity for exactly this medium. A medium that can
oscillate with any arbitrary frequency would be the best choice, so that the medium
itself would not be the cause for any frequency distorsions. In Chap. 4, we described
that the mechanical continuum, the limiting case of the linear chain, is just such
a medium. Here, waves of any frequency can propagate dispersion free, in other
words with a velocity independent of frequency, for example with the transversal
sound velocity c T . Our mechanical continuum is therefore ideal for our purposes.