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Doppler Effect
(xkcd.com)
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The frequency shift is caused by the Doppler effect. The magnitude of that shift is a function of the speed at which something is moving relative to the observer. The distance of a galaxy is also a function of that speed, since it'll be determined by how quickly it's been moving away from us for some period of time. Result: the two are correlated.
Also, US rumbler sirens are amazing.
https://www.youtube.com/watch?v=OAtqbXO_PM8