Notes p.42
The Expanding Universe
1. Doppler Effect
Additional reading: Higher Physics for CfE, p.70-72.
Watch or listen to the following video clips:
http://physics.wfu.edu/demolabs/demos/3/3b/3B40xx.html
http://www.animations.physics.unsw.edu.au/jw/doppler.htm
http://www.animations.physics.unsw.edu.au/jw/doppler.htm#source
Notes p.42
The Expanding Universe
1. Doppler Effect
Objects Moving Towards Us
We are all familiar with the “nee naw” sound from
approaching emergency vehicles.
As the vehicle approaches, the sound we hear is
higher in pitch than when the vehicle is
stationary .
This is because, as the sound source moves
towards us, the sound wavelength it emits gets
“squashed”. This shortening of wavelength is
detected as a sound with higher frequency (or
“pitch”).
The sound waves are distorted like this…
stationary source
moving source
stationary
observer
The change in the “observed” frequency is what
we call “The Doppler Effect”.
The Doppler Effect is observed with sound and
light, as well as with other waves.
Blue Shift
We can observe the Doppler Effect in galaxies.
Obviously we don’t hear light, but we can detect a
change in their spectral lines (showing the e.m.
wavelengths emitted).
If the galaxy is moving towards our Milky Way,
the spectra is shifted towards higher
frequencies and shorter wavelengths. We call
this a “Blue Shift”.
This is currently the case with
our neighbouring galaxy, Andromeda.
No need to worry – it’s
2.5 million light years away!
Objects Moving Away From Us
As an emergency vehicle moves away from us, the
sound we hear is lower in pitch than for the
stationary vehicle.
This is because, as the sound source moves away
from us, the sound wavelength it emits gets
“stretched”.
This lengthening of wavelength is detected as a
sound with lower frequency (or “pitch”).
Red Shift
As stars and galaxies move away from us (that’s
most of them!) we detect a change in their
spectral lines towards lower frequencies and
longer wavelengths. We call it a “Red Shift”.
Light from most galaxies and stars is “red
shifted”, so scientists believe that the Universe
is expanding. This is strong evidence for The Big
Bang Theory, coming up in this course very soon!
Note … localised gravity can explain the blue
shift for Andromeda.
Red Shift and Blue Shift Images
1.
2.
Colour your notes to emphasise the shifts.
What can you say about Galaxies A, B and
C below?
Doppler Effect Calculations
fs = source frequency in Hz
fo = observed frequency in Hz
v = velocity of the sound or light in ms-1
vs = velocity of the source in ms-1
For a sound or light source moving towards a
stationary observer:
v
fo = fs
(v – vs)
For a sound or light source moving away from a
stationary observer:
v
fo = fs
(v + vs)
IMPORTANT NOTE
These Doppler Effect equations cannot be used
for very fast moving sources because
relativistic effects would be substantial.
By “very fast” or “relativistic speeds” we
generally mean speeds over 10% of the speed
of light or over 3 x 107 ms-1 or over 0.1c.
The Higher course doesn’t cover these
calculations … BIG PHEW!!!
Worked Examples
Worked Example 1
A police car siren emits sound with a frequency of
1000 Hz. The speed of sound in air is 340 ms-1.
a)
Determine the frequency observed by a
stationary pedestrian if the police car is
moving towards the pedestrian at 20 ms-1.
fo
fs
v
vs
=
=
=
=
?
1000 Hz
340 ms-1
20 ms-1
fo = fs
v
(v - vs)
= 1000
340
(340 - 20)
= 1063 Hz
4 sig figs is 1 too many…1060
Hz is acceptable.
Worked Examples
Worked Example 1
A police car siren emits sound with a frequency of
1000 Hz. The speed of sound in air is 340 ms-1.
b)
Determine the corresponding wavelength of
sound detected by the observer.
v = 340 ms-1
fo = 1063 Hz
lo = ?
lo =
v
fo
= 340
1063
= 0.32 m
Worked Examples
Worked Example 2
A 410 nm spectral line from Hydrogen is examined
in a laboratory on Earth. A stellar spectrum shows
this line as red shifted to 440 nm
a)
Calculate the frequency of the spectral line
from the Hydrogen source examined in the
laboratory.
v
v = 3 x 108 ms-1
fs =
ls
fs = ?
8
ls = 410 x 10-9 m
3
x
10
=
410 x 10-9
= 7.32 x 1014 Hz
Worked Examples
Worked Example 2
A 410 nm spectral line from Hydrogen is examined
in a laboratory on Earth. A stellar spectrum shows
this line as red shifted to 440 nm
b)
Calculate the frequency of the spectral line
recorded in the stellar spectrum.
v = 3 x 108 ms-1
fo = ?
lo = 440 x 10-9 m
fo =
v
lo
8
3
x
10
=
440 x 10-9
= 6.82 x 1014 Hz
Worked Examples
Worked Example 2
A 410 nm spectral line from Hydrogen is examined
in a laboratory on Earth. A stellar spectrum shows
this line as red shifted to 440 nm
c)
Without relativistic considerations,
determine the velocity of the star.
v
fo = fs
fo = 6.82 x 1014 Hz
(v + vs)
14
fs = 7.32 x 10 Hz
3 x 108
6.82 x 1014 = 7.32 x 1014
v = 3 x 108 ms-1
(3 x 108 + vs)
2.196 x 1023
8
vs = ?
(3 x 10 + vs) =
6.82 x 1014
vs
=
3.22 x 108 - 3 x 108
= 2.2 x 107 ms-1
“Redshift” Quantified
Edwin Hubble noticed, way back in the 1920s,
that light from the stars and galaxies he
observed was red shifted. So he presumed all
stars and galaxies were moving apart.
He quantified the redshift (z) as “the ratio of
the change in wavelength to the wavelength with
the source at rest”.
In short …
z = lo - lrest
lrest
Of course later it was discovered that some stars
and 1 galaxy are actually moving towards us.
In this case the redshift value, z, is negative.
So a negative “redshift” is, in fact, a blue
shift.
For non-relativistic speeds (that’s less than
about 10% of the speed of light, or 0.1c), the
redshift of a star or galaxy can be simplified to
z =
v
c
Worked Example 3
Consider again the Hydrogen line fromWorked
Example 2. 410nm recorded in the lab and 440nm
observed from a star.
a)
Calculate the redshift value, z.
z = ?
lrest = 410 x 10-9 m
lo = 440 x 10-9 m
z =
lo - lrest
lrest
-9
30
x
10
=
410 x 10-9
= 0.073
Worked Example 3
Consider again the Hydrogen line fromWorked
Example 2. 410nm recorded in the lab and 440nm
observed from a star.
b)
Assuming the star is moving with a nonrelativistic velocity, determine its
recessional velocity.
z = 0.073
c = 3 x 108 ms-1
v = ?
z =
v
c
0.073 = v
3 x 108
vgalaxy = 0.073 x 3 x 108
= 2.2 x 107 ms-1
Worked Example 3
Consider again the Hydrogen line from Worked
Example 2. 410nm recorded in the lab and 440nm
observed from a star.
c) How does your answer compare with Worked
Example 2c)?
Answers are the same 
Complete Problems from Tutorial IV
The Expanding Universe Q. 1 – 20
Answers
1. A = higher, B = lower, C D= Doppler Effect
a) fo = fs
v
(v – vs)
12. 3060 ms-1
b) fo = fs
v
(v + vs)