- Recall the Doppler effect is defined as:
The apparent change in wavelength or frequency of the radiation from a source due to its relative motion away from or toward the observer
- On Earth, the Doppler effect is most easily observed when something which is both fast moving and emitting a loud sound (such as an ambulance or fast car) moves past an observer, producing a characteristic change in the pitch of the sound that is heard
- In space, the Doppler effect of light can be observed when spectra of distant stars and galaxies are observed, this is known as:
- Redshift if the object is moving away from the Earth, or
- Blueshift if the object is moving towards the Earth
- Redshift is defined as:
The fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other
- For non-relativistic galaxies, Doppler redshift can be calculated using:
- Δλ = shift in wavelength (m)
- λ = wavelength emitted from the source (m)
- Δf = shift in frequency (Hz)
- f = frequency emitted from the source (Hz)
- v = speed of recession (m s-1)
- c = speed of light in a vacuum (m s-1)
The spectra below show dark absorption lines against a continuous visible spectrum.
A particle line in the spectrum of light from a source in the laboratory has a frequency of 4.570 × 1014 Hz.
The same line in the spectrum of light from a distant galaxy has a frequency of 4.547 × 1014 Hz.
a) What speed is the distance galaxy moving in relation to the Earth?
b) Is it moving towards or away from the Earth?
Step 1: Write down the known quantities
- Emitted frequency, f = 4.570 × 1014 Hz
- Shift in frequency, Δf = (4.547 – 4.570) × 1014 = –2.3 × 1012 Hz
- Speed of light, c = 3.0 × 108 m s–1
Step 2: Write down the Doppler redshift equation
Step 3: Rearrange for speed v, and calculate
Step 1: Compare the frequencies and answer the question
- The observed frequency is less than the emitted frequency (the light from a laboratory source),
- The source is receding (moving away from) from the Earth
In your exam, be sure to emphasise that redshift means the wavelength of spectral lines increases towards the red end of the spectrum, do not say that the spectral lines become red, as this is incorrect.