Seismic Wave
A seismic wave is a wave of energy that travels through or along Earth from an earthquake, explosion, or other source of ground vibration.
Definition
Seismic waves are the vibrations that spread out through the ground from an earthquake, like ripples crossing a pond, and the fastest ones travel through Earth at more than $8$ kilometers per second. Body waves travel through the interior: P-waves are compressional and fastest, moving through solids and liquids, while S-waves are slower shear waves that pass only through solids; surface waves such as Love and Rayleigh waves travel along the ground, arrive last, and cause the most damage. Wave speed depends on the rock's elastic moduli and density, $v_P = \sqrt{\frac{K + \frac{4}{3}\mu}{\rho}}$ and $v_S = \sqrt{\frac{\mu}{\rho}}$, and because shear modulus $\mu$ is zero in fluids, S-waves vanish inside liquid regions, which is how their absence beyond $104^\circ$ from an earthquake revealed the liquid outer core.
Example
If an earthquake happens in California, sensitive instruments in North Carolina can pick up the waves minutes later, having passed straight through the planet. P-waves move at about $6\ \text{km/s}$ in the crust and S-waves at about $3.5\ \text{km/s}$, so a $30$-second gap between their arrivals at a station means the earthquake was roughly $250\ \text{km}$ away. Inge Lehmann used exactly this kind of timing in 1936, finding faint P-wave arrivals inside the shadow zone that could only be explained by reflection off a solid inner core, and modern earthquake early warning systems use the first seconds of P-wave data to send alerts before the more destructive S-waves and surface waves arrive.
Key Insight
S-waves cannot pass through liquid, so they disappear on the far side of Earth from a large earthquake, and that shadow zone is the main evidence that the outer core is liquid. Seismic waves are essentially the only direct probe of Earth's deep interior: nearly everything known about the mantle and core, from layer depths to the state of the outer core, comes from how these waves speed up, slow down, bend, or vanish as they travel.