Uses of The Doppler Effect

The Doppler effect is important in many key areas of science including:
- Radar readings for moving objects
- Measuring the rate of blood flow within a patient
- Finding planet orbits around distant stars
- Mapping the expansion of the universe

Redshift of EM Radiation

On Earth, the Doppler effect of sound can be easily observed when sound waves move past an observer at a notable speed
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:

\frac{Δ λ}{λ} = \frac{Δ f}{f} = \frac{v}{c}

Where:

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)

Worked example

The spectra below show dark absorption lines against a continuous visible spectrum.

Redshift, downloadable AS & A Level Physics revision notes

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.

Calculate the speed of the distant galaxy in relation to the Earth. Determine whether it is moving towards or away from the Earth.

Step 1: Write down the known quantities

- Received frequency, f_r = 4.547 × 10¹⁴ Hz
- Original frequency, f₀ = 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

\frac{Δ f}{f_{0}} = \frac{v}{c}

Step 3: Rearrange for speed v, and calculate

v = \frac{c Δ f}{f_{0}} = \frac{(3.0 \times 10^{8}) \times (2.3 \times 10^{12})}{4.570 \times 10^{14}}

= 1.5 × 10⁶ m s^–1

Step 4: Write a concluding sentence

- The observed frequency is less than the emitted frequency (the light from a laboratory source), therefore, the source is receding, or moving away, from the Earth at 1.5 × 10⁶ m s^–1

An Expanding Universe

After the discovery of Doppler redshift, astronomers began to realize that almost all the galaxies in the universe are receding
This led to the idea that the space between the Earth and the galaxies must be expanding
This expansion stretches out the light waves as they travel through space, shifting them towards the red end of the spectrum
The more red-shifted the light from a galaxy is, the faster the galaxy is moving away from Earth

Expanding Universe Balloon

The expansion of the universe can be compared to dots on an inflating balloon

As the balloon is inflated, the dots all move away from each other
In the same way as the rubber stretches when the balloon is inflated, space itself is stretching out between galaxies
Just like the dots, the galaxies move away from each other, however, they themselves do not move

Uses of The Doppler Effect (DP IB Physics: HL)

Revision Note