The Doppler effect for sound and light, redshift of distant galaxies, Hubble's law and the age of the universe, and the evidence supporting the Big Bang.

What this key area is asking

The SQA wants you to apply the Doppler effect to sound and light, explain the redshift of distant galaxies as evidence of expansion, use Hubble's law to relate recession speed and distance (and estimate the age of the universe), and outline the evidence for the Big Bang.

The Doppler effect

The classic example is a passing siren or racing car: the pitch is higher as it approaches and drops as it recedes. The same idea applied to light gives redshift and blueshift.

Redshift and Hubble's law

For light from a moving source the fractional shift in wavelength is the redshift $z$:

Edwin Hubble found that more distant galaxies recede faster, and that the recession speed is proportional to distance:

Evidence for the Big Bang

Three main lines of evidence support a hot, dense beginning. First, the redshift of distant galaxies in every direction shows the universe is expanding from a common origin. Second, the cosmic microwave background radiation is the cooled remnant of the hot early universe, observed as a near-uniform microwave glow at about $2.7\ \text{K}$. Third, the measured abundance of light elements (hydrogen and helium) matches what nucleosynthesis in the first minutes of a hot Big Bang predicts.

Examples in context

Speed cameras and weather radar use the Doppler shift of reflected radio waves to measure how fast a car or a raindrop is moving. Astronomers measure the redshift of spectral lines from galaxies to find their recession speeds and map the expansion of the universe. The discovery of the cosmic microwave background by Penzias and Wilson, an unexpected uniform microwave hiss from all directions, was the decisive evidence that tipped opinion in favour of the Big Bang over a steady-state universe. Medical ultrasound uses the Doppler effect on sound to measure blood flow. In each case a frequency shift is read as a velocity.

Try this

Q1. State what happens to the observed frequency of a sound when its source moves towards you. [1 mark]

• Cue. The observed frequency increases (the pitch rises).

Q2. A galaxy recedes at $1.5 \times 10^{7}\ \text{m s}^{-1}$. Calculate its redshift. Take $c = 3.0 \times 10^{8}\ \text{m s}^{-1}$. [2 marks]

• Cue. $z = \frac{v}{c} = \frac{1.5 \times 10^{7}}{3.0 \times 10^{8}} = 0.050$.

Q3. State one piece of evidence, other than galactic redshift, that supports the Big Bang. [1 mark]

• Cue. The cosmic microwave background radiation (or the observed abundance of hydrogen and helium).