Theme 5 – The Doppler Shift
ASTR 101
Prof. Dave Hanes
The Surfer’s Experience
Waves come in to shore
perfectly regularly.
If you float in place, you bob up
and down as each wave passes
– say, once every 5 sec
If you paddle out towards the
incoming waves, you meet each
wave sooner than expected, so
your frequency of bobbing up
and down increases – perhaps
once every 4 seconds
Think of Sound
The ‘wavefronts’ reach your ear
with a regular frequency.
But if you walk towards the
speaker, successive waves hit
your eardrum a little sooner than
expected, so they arrive with a
higher frequency than expected.
Your eardrum is set vibrating at a
higher frequency than if you were
at rest! The tone sounds higher
in pitch than if you were at rest.
Turn The Thinking Around
If the surfer now paddles towards the shore, the waves affect
her with reduced frequency. (In the limit, she ‘rides a wave’ and
experiences no up and down motion at all!)
If the listener walks away from the speaker, the sound waves
arrive less frequently, producing a lower-pitched sound.
Moreover, it does not matter if the listener is moving and the
speaker at rest, or vice versa. Relative motion is the key! If the
distance between them is shrinking, the perceived frequency is
increased; if it’s growing, the perceived frequency drops.
The Doppler Effect in Words
Any periodic effect will be:

Perceived at higher frequency if the distance
between the source and the receiver is
decreasing

Perceived at reduced frequency if the distance
between the source and the receiver is
increasing
A Direct Test: Sound
Doppler proposed a test: an open
train car with trumpeters playing
a note of constant pitch.
Other musicians with ‘perfect pitch’
stood beside the tracks to see if
the note sounded ‘too high’ as the
train approached.
This was successful!
http://www.planetseed.com/relatedarticle/doppler-effect-train
Common Misunderstandings
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If you know the expected pitch, and you hear a note that is “too
high,” you know instantly that the source is approaching. You don’t
need to hear it again later to see if anything changes. One hearing
is enough!
The familiar up-and-down wailing of a siren is not the Doppler shift!
(Is the source alternately coming towards you and moving away?
No!) But here’s a link where we hear that wailing (produced by the
siren itself) and then an overall drop in pitch as the fire engine
passes by (so it is no longer approaching you but receding).
https://www.youtube.com/watch?v=imoxDcn2Sgo
What is Light?
You are right: it’s a wave, the crests of which reach you
with a certain frequency.
By Doppler’s reasoning, if you are moving towards a source
of (say) red light, you should perceive a higher frequency –
the light should look somewhat bluer.
And conversely: a receding source should look somewhat
redder. (This is true whether it is you or the source that is
‘actually moving.’ Relative motion is the key.)
A Losing Argument
You run a red light, but tell the traffic policeman that you
perceived it as green because you were approaching it.
This would require you to be travelling at a considerable
fraction of the speed of light! So you get charged with
speeding instead.
One Problem
Doppler first applied this reasoning to stars. Some binary
stars have a red and a blue star side by side. He proposed
that the colours might be due to their motions – the blue
one approaching us, the red one moving away.
But the speed of light is so high,
and the velocities of the stars so
small, that only imperceptible colour
changes could ever arise. (As you
now know, the difference is because
of different stellar temperatures.)
Apparently Hopeless
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As noted, the colours of stars are too little affected by
the Doppler shift to be noticeable, since their velocities
though space are so small (perhaps a few hundred
km/sec) compared to ‘c’ (300,000 km/sec).
Moreover, even if blue light in the spectrum were to be
shifted to (say) green, previously invisible ultraviolet
light will be shifted to blue, making up the loss.
All in all, you expect no pronounced effect, and indeed this
is hopeless for determining velocities.
Easy With Emission Lamps!
Someone turns on an emission lamp. The spectrum might
look like this (one blue, one green, one red line):
Suddenly, in a fit of rage, they hurl it at your head at very
high speed. To you, the spectrum now looks like this:
Because you can identify several discrete lines, the shift
towards the blue/violet end is actually noticeable! (even for
modest velocities).
Towards
and
Away
Same Principle for the Stars
Instead of looking at the overall colours of the stars, we
look for displacements in the absorption lines. Measuring
those displacements gives us the velocities of the stars
relative to us.
Note that one measurement only is required to figure out
the instantaneous velocity – there’s no need to “do it
again later and look for changes.”
Note also that this does not tell you anything about the
sideways motion of a star – only its motion along the
line of sight (the so-called radial velocity).
Applied Here
First, we use an emission lamp at rest in the observatory
to tell us what colour / wavelength / frequency each line
should be, then compare the star’s spectrum to that.
We don’t need to see the colours, by the way! We note
that the absorption lines are shifted to the blue end
(shorter wavelengths, higher frequencies.) This tells us
that the star is approaching (or that we are moving
towards it). And we can determine that velocity!
Arcturus
Remember that the radial velocity signifies only the relative
motion – it could be the Earth or the star moving (or both).
Here’s the spectrum of Arcturus in June
And here it is in December
Compare These in Detail
We see a change in the Doppler shift, implying
a change in velocity from June to December.
This behaviour repeats, year after year.
Is Arcturus moving back-and-forth in our direction?
NO! In this case, we are noticing the back-and-forth motion of
the Earth towards and away from Arcturus as we orbit the Sun.
The Doppler shift told us about the relative motion.
Radar Guns and Sunlight
In the Solar System, we can use the Doppler effect as well,
in one of two ways:
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Like a policeman, send out actual radar signals. This is
a radio wave of a fixed frequency that gets shifted to a
higher or lower frequency if the object off of which it
reflects is moving towards or away from us
Use the Sun as a source (a ‘radar gun’)! When its light
reflects from an object, we see a Doppler shift in the
absorption lines in the solar spectrum depending on how
the object is moving.
Applied to Saturn’s Rings
Look at the sunlight reflected
from various parts of Saturn.
The planet itself rotates as
a whole, with the outer edges
moving fast (one towards us,
the other away)
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The rings are different. The inner edge of the ring moves
faster than the outer edge! This would not be possible if it
were solid, like a frisbee. The rings are evidently made of
small lumps, like millions of tiny moons in parallel orbits.