The Doppler Effect
A duck will make a circular pattern of waves as it sits on the pond.
When it swims it is moving away from the waves behind and towards the waves in front. The waves in front are bunched up, the wavelength is shorter.
In the same way the noise from a stationary car will spread out symmetrically in all directions. If the car is driven fast then the sound waves behind are stretched out and those in front are bunched up. If you listen to a fast car going past you then the note changes. It is higher as it approaches and slightly lower when it has passed.
This diagram is exaggerated. The car would have to be traveling very fast for the sound waves to bunch up this much.
Early last century astronomers examining light from distant galaxies noticed that in most cases the patterns were shifted into the red end of the spectrum. The characteristic lines of absorption spectra stayed in the same pattern but were shifted into different colours. They concluded that the longer wavelengths meant that these galaxies are moving away from us. They have to be moving very fast to cause this change to light waves which travel at 300,000,000 m/s. We can see this shift in the colour spectrum of stars in our own galaxy particularly in binary stars rotating fast around one another.
The explanation we use for red shift between galaxies now is not quite the same. The change in colour is the effect of space between the galaxies stretching as the Universe expands. The maths calculating the rate at which the distances are increasing is nevertheless, much the same.
Light from our own sun or stars in our own galaxy at the top
Light from distant galaxies at the bottom. The black lines are moved towards the red colours.
The further away the galaxies the greater the “red shift”. This is evidence in favour of the “big bang theory”.