The doppler effect, the expanding Universe, and red shift
Starter: what is meant by the Doppler effect?
Explanation
Doppler Effect (sound)
When the source is moving towards you, the sound you hear is of a higher pitch. This is called the perceived frequency
The Doppler Effect
A source moves towards observer B and away from observer A.
Deriving the formulae
In this diagram the wavelength and frequency appear the same to each observer
Deriving the formulae
For a moving source after time = T
Deriving the formulae
As distance = speed x time, the distance from A to the source is:
The distance from B to the source is:
Deriving the formulae
As wavelength = speed/frequency, the wavelength at A is:
the wavelength at B is:
Deriving the formulae
As f’ = speed/wavelength’, the perceived frequency at A is:
the perceived frequency at B is:
Deriving the formulae
If the source is stationary and observer A moves away, and B closer. The same pathway gives a perceived frequency at A:
the perceived frequency at B:
Finally the data book versions we use
If you are not sure which to use, just do the calculation and ask the question - should the frequency increase or decrease in this context?
Applications
Measuring the speed of moving objects (like cars or baseballs)
Measuring the speed of flow of blood cells in an artery
Example
A car is moving at a speed of 34 m s-1 towards a stationary source of sound emitting a note of constant frequency of 5.0 kHz. What frequency will be observed by the people in the car? The speed of sound in air is 340 m s-1.
Example
A car is moving at a speed of 34 m s-1 towards a stationary source of sound emitting a note of constant frequency of 5.0 kHz. What frequency will be observed by the people in the car? The speed of sound in air is 340 m s-1.
f’ = f(v + u0)/v
Example
A car is moving at a speed of 34 m s-1 towards a stationary source of sound emitting a note of constant frequency of 5.0 kHz. What frequency will be observed by the people in the car? The speed of sound in air is 340 m s-1.
f’ = f(v + u0)/v = 5000(340 + 34)/340 = 5500 Hz
Example
A galaxy is moving away from the Earth at a speed of 3.0 x 105 m s-1. If the light emitted from the galaxy has a frequency of 6.0 x 1014 Hz, find the frequency of light received on Earth.
Example
A galaxy is moving away from the Earth at a speed of 3.0 x 105 m s-1. If the light emitted from the galaxy has a frequency of 6.0 x 1014 Hz, find the frequency of light received on Earth.
f’ = f v/(v + u0) = (3.0 x 108 x 6.0 x 1014)
(3.0 x 108+ 3.0 x 105 )
= 5.99 x 1014 Hz
Mini-Plenary
The two sources represent a fire engine. The first is standing still the second moving to the right. Explain why the pitch of the fire engine changes as it is coming towards the observer and when it is then moving away. Try to include all of the following words in your explanation:
Frequency, pitch, wavelength, squashed, stretched, towards, away
Example
a. calculate the change of frequency which will be detected by a police speed gun using a frequency of 20.6 GHz, when it is directed at a car moving directly away at a speed of 130 km h−1 (36.1 m s−1).
b. state what change of frequency would be detected if
the vehicle was moving directly towards the speed
gun, at the same speed.
Example
a. calculate the change of frequency which will be detected by a police speed gun using a frequency of 20.6 GHz, when it is directed at a car moving directly away at a speed of 130 km h−1 (36.1 m s−1).
b. state what change of frequency would be detected if
the vehicle was moving directly towards the speed
gun, at the same speed.
Red Shift (EM wave)
The picture above shows the EM spectrum. Right in the middle we have visible light which is part of the spectrum produced by stars. So what would happen to the light from a star if the star was moving towards you?
Red Shift
Stars that are easy to see produce mainly yellow light. If a star was to move away from us, the wavelength of the light would increase. This would make the light appear redder!
Red Shift
True or False
Copy these sentences into the google form and correct the ones that are incorrectly written
What is happening?
Astronomers use Doppler shifts to calculate precisely how fast stars and other astronomical objects move toward or away from Earth.
Actual data rather than exam questions…
But what are the lines/reference points?
Spectra matching task
The doppler effect in light
The doppler effect formula
An example of Doppler shift from 2 galaxies
Some practice – ws7
λ (Earth) nm | λ (Observed) nm | Δλ nm | v / ms-1 | Blue / Red Shifted | Direction of motion relative to Earth |
410.3 | 411.2 | | | | |
382.2 | 378.4 | | | | |
314.3 | 324.6 | | | | |
421.6 | 431.5 | | | | |
453.7 | 436.7 | | | | |
510.1 | 500.5 | | | | |
492.7 | 500.6 | | | | |
316.4 | 356.7 | | | | |
562.1 | 602.0 | | | | |
478.9 | 443.2 | | | | |
Ws 7 solutions
λ (Earth) nm | λ (Observed) nm | Δλ nm | v / ms-1 | Blue / Red Shifted | Direction of motion relative to Earth |
410.3 | 411.2 | 0.9 | 6.5e5 | Red | Away |
382.2 | 378.4 | -3.8 | 3.0e6 | Blue | Towards |
314.3 | 324.6 | 10.3 | 9.8e6 | Red | Away |
421.6 | 431.5 | 9.9 | 7e5 | Red | Away |
453.7 | 436.7 | -17 | 1.12e7 | Blue | Towards |
510.1 | 500.5 | -9.6 | 5.6e6 | Blue | Towards |
492.7 | 500.6 | 7.9 | 4.8e6 | Red | Away |
316.4 | 356.7 | 40.3 | 3.8e7 | Red | Away |
562.1 | 602.0 | 39.9 | 2.1e7 | Red | Away |
478.9 | 443.2 | -35.7 | 2.2e7 | Blue | Towards |
Why standing waves?
Suggest that the red-shift of light from galaxies indicates that the universe is expanding.
“The sky is dark at night”
Why does this pose a problem for the idea of an infinite (time and space) universe?
Olber’s paradox
Cosmological redshift (z)
CMBR
In 1960 two physicists, Dicke and Peebles, realising that there was more He than it could be produced by stars, proposed that in the beginning of the Universe it was at a sufficiently high temperature to produce He by fusion.
It was predicted that the actual photons from this original high energy, high temperature radiation would today have a maximum λ corresponding to a black body spectrum of 2.76K, we would be looking for microwave radiation.
The discovery of cosmic microwave background (CMBR) radiation by Penzias and Wilson.
Shortly after this prediction, Penzias and Wilson were working with a microwave aerial and found that no matter in what direction they pointed the aerial it picked up a steady, continuous background radiation.
The discovery of cosmic microwave background (CMBR) radiation by Penzias and Wilson.
This radiation is essentially a black body with temperature of 2.76 K, which peaks in the microwave portion of the spectrum.
The discovery of cosmic microwave background (CMBR) radiation by Penzias and Wilson.
All galaxies move away from each other, which is in accordance with the cosmological principle. So galaxies don’t fly apart, it is the space between them that increases.
The reason why the wavelength of light from distant galaxies is increased is because during the time taken for the light to travel from the galaxy to the Earth the space has expanded, so stretching the wavelength. This is called cosmological redshift.
Cosmological redshift (z)
In 1920’s Edwin Hubble and Milton Humanson realised that the spectra of distant galaxies showed a redshift, which means that they are moving away from Earth.
So, if galaxies are moving away from each other then they may have been much closer together in the past.
Why is Doppler effect so important?
Main evidence that we will meet in our course:
Big Bang
Expanding Universe - Cosmological redshift
Hubble and Slipher discovered that all galaxies were moving away from the Earth and presented a red shift.
At very large distances, the recessional velocity will be faster than the speed of light.
But according to Einstein’s general relativity an expanding Universe will have expanding space, so the galaxies aren’t moving apart through space; it is the space they are in that is expanding.
This also explains why the further galaxies recede faster.
Using measurements made by Edwin Hubble up to 1929 the speeds of distant galaxies were found from red-shifts:
(The distances were determined by comparing Cepheid variables with standard candles, or by guesswork.)
v ∝ d
Hubble’s law and expansion
If speed is proportional to distance what would you expect the constant of proportionality to be related to?
Using measurements made by Edwin Hubble up to 1929 the speeds of distant galaxies were found from red-shifts:
(The distances were determined by comparing Cepheid variables with standard candles, or by guesswork.)
v ∝ d
so v = H0 d
Hubble’s law and expansion
(The distances were determined by comparing Cepheid variables with standard candles, or by guesswork.)
This relationship is useful to see but not part of our course
Limitations of Hubble’s law.
It is constant in space but varies with time. This means that the rate of expansion of the Universe was not the same throughout its expansion.
There are uncertainties in the distances measured precisely because it is quite difficult to measure distances to remote galaxies accurately.
If speed = distance/time and speed = Hubble’s constant x distance then surely Hubble’s constant and time are related.
We define T as Hubble Time.
Calculate the Hubble Time using the value for the Hubble constant of: 70 ± 1 (km s-1) Mpc-1
(NASA: tests of big bang expansion)
Deduce Hubble Time. - a nice extension to the idea of red shift
What is the red-shift of a galaxy with a recession speed of:
a 2.2 × 106 ms–1?
b 10% of the speed of light?
What is the recession speed of a galaxy (kmh–1) if radiation of original wavelength 6.5 × 10–7m undergoes a change in wavelength of 3.7 × 10–8 m?
A star receding at a velocity of 9.2 × 103 km s–1 emits radiation of wavelength 410 nm. What is the change in wavelength due to the red-shift of this radiation when it is received on Earth? Then calculate its received wavelength?
Hydrogen emits radiation of frequency 6.17 × 1016 Hz. What frequency will be detected on Earth from a galaxy moving away at 1.47 × 107 m s–1?
Red Shift Questions