Download Doppler Effect • The Doppler Effect is the change in frequency

Doppler Effect
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The Doppler Effect is the change in frequency observed when a source of sound waves is
moving relative to an observer.
Examples of the Doppler effect are:
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Hearing an increase in a car horn’s pitch as the car approaches you
Hearing an increase then decrease the pitch of a jet’s engine noise as it passes you
Sound source moving relative to a stationary observer
Sound source moving towards stationary observer – frequency is increased:
Sounds source moving away from stationary observer – frequency is decreased:
Example
A police car siren emits sound of frequency 40 Hz.
The police car travels towards an observer at 20 ms-1.
Calculate the frequency heard by the observer.
(Speed of sound in air = 340 ms-1)
Solution
fobs = ? v = 340 ms-1
vs = 20 ms-1
Redshift and Hubble’s Law
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Redshift is an example of the Doppler Effect.
It is the term given to the change in frequency of the light emitted by stars, as observed
from Earth, due to the stars moving away from us.
Redshift has always been present in the light reaching us from stars and galaxies but it was
first noticed by astronomer Edwin Hubble, in the 1920’s, when he observed that the light
from distant galaxies was shifted to the red end of the spectrum.
The extent of redshift is given by:
where:
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z = extent of redshift
observed = observed wavelength of light (for example the wavelength seen by an observer on
Earth viewing a distant star)
rest = wavelength of light if the object is at rest
For galaxies moving at non-relativistic speeds, the extent of redshift can also be calculated using:
where:
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z = extent of redshift
v = speed of galaxy
c = speed of light in vacuum 3x108 ms-1
Example
Light from a distant galaxy is found to contain the spectral lines of hydrogen. One line has a
wavelength measured as 466 nm. When the same line is observed from a hydrogen source on Earth
it has a wavelength of 434 nm.
a) Calculate the extent of redshift, z, for this galaxy.
b) Calculate the speed at which the galaxy is moving relative to the Earth.
Solution
a)
b)
Hubble’s Law
Hubble’s Law describes the relationship between the velocity of a galaxy, as it moves away from us,
and its distance.
v = Ho d
where:
v = velocity of galaxy (ms-1)
H0 = Hubble constant (quoted as 2·3 × 10–18 s–1)
d = distance between the galaxy and us (m)
Example
A galaxy is moving away from the Earth at a speed of 0·074 c.
a) Convert 0·074 c into a speed in ms-1.
b) Calculate the approximate distance, in metres, of the galaxy from the Earth.
Solution
(a)
(b)
Hubble’s Law and Age of the Universe
By working back in time it is possible to calculate a time when all the galaxies were at the same point
in space. This allows the age of the universe to be calculated.
v = speed of galaxy receding from us
d = distance of galaxy from us
H0 = Hubble’s constant
t = time taken for galaxy to reach that distance, i.e. the age of the universe
t=d/v
So
but from Hubble’s Law, v = Hod
t = d / Hod
t = 1 / Ho
t = 4.347 x 1017 seconds
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Convert this time to years (divide by 365x24x60x60)
Age of Universe = 1.37 x 1010 years
13.7 billion years (1 billion = 1 x109)
Gravity and expansion
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Gravity is an attractive force between two objects with mass
You would expect, therefore for gravity to slow down the rate of expansion and pull the
galaxies closer together
This is not what is observed however. Redshift tells us that the galaxies are moving further
apart
Other observations lead to the conclusion that the rate of expansion is in fact increasing
There must be other factors at work which overcome the force of gravity
Fate of the Universe
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No one is sure about the eventual fate of the Universe
It could
o Continue expanding forever
o The expansion rate could decrease and be left in a steady-state
o The expansion could reverse and the galaxies could start moving closer together
What is known is that the eventual fate of the Universe will depend on the overall mass
Orbital speed of stars and mass of galaxies
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A star’s orbital speed is determined almost entirely by the gravitational pull of matter inside
its orbit
This means that the mass of a galaxy can be determined by the orbital speeds of stars within
it
Dark Matter
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Measurements of the mass of our galaxy and others lead to the conclusion that there is
significant mass that cannot be detected
This “missing” mass is called dark matter
The majority of mass in the Universe is dark matter
Dark Energy
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As stated above, the expansion rate of the Universe is increasing – something is overcoming
gravitational attraction
The name given to whatever is responsible for the increasing expansion rate is dark energy