Most of what we know about Earth’s core comes from earthquakes. When an earthquake happens, it sends sound waves through the ground so powerful that sensitive instruments can detect them from all the way on the other side of the planet. Just like how light refracts and lenses while going through materials of different densities, the core of the Earth works like a lens bending the sound waves that pass through it in a very specific way. By measuring these sound waves, it’s possible to work out a lot of very precise detail about Earth’s core including what state of matter it is.
Earthquakes generate different kinds of seismic waves that behave differently when passing through different materials. Notable, one of the types of waves (S waves) don’t pass through liquids. This creates a kind of “shadow” that tells us that part of the core is liquid. But the behavior of the other kind of waves (P waves) also tells us that there is something solid inside that liquid.
Here is a picture for reference:
[https://akm-img-a-in.tosshub.com/indiatoday/images/story/201602/seismic-waves-650_042715041742.jpg](https://akm-img-a-in.tosshub.com/indiatoday/images/story/201602/seismic-waves-650_042715041742.jpg)
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