So, sound (and light*) are a wave, yes? they have pluses of power, a waveform, with a wavelength and frequency. If you make that wave go “faster”, your getting more waves per second, so your frequency has gone up, and your wavelength must be shorter.
Imagine a racecar passing by you at, say 120mph, with that classic “neeee-OWW” sound as it speeds past you. The engine is actually putting out the same noise the whole time, but what you hear is affected by the relative speeds between you and the car.
as the car approaches you, the sound is travling at its based speed, but the car is moving as well, so its “catching up” to its own sound. this means the sound is getting squashed together a bit, which means that when it reaches your ear, it sounds higher pitched because the frequency is higher. once its past you, the waves are more spread out, becuase the car is moving away, so the wavelength is longer, so the engine sounds lower pitched.
now, with light, when you change the wavelength like this, you change the colour of light. you go up and down the classic “roy g biv” rainbow sprectum, with red being the slower end and blue being the faster end.
so, if you know what colour a thing “should” be, based on something like spectral absorption**, you can use this shift to work out how fast something is moving towards or away from us.
*yes, I know about light’s wave particle duality, its *complicated*, i’m glossing over it for ELI5.
** basicaly, some elements absorb light in specific patterns (say, 1 gap, then 2 very close together, then 1 gap), and these patterns stay the same relative to each other, regardless of where they are on the spectrum. So, if you see that specific 1-2-1 pattern of gaps on the spectrum, you know “ah, those are the hydrogen lines, they should be *here*, so we’ve shifted by that amount”
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