The seismic wave type that cannot travel through Earth’s liquid outer core is the S-wave.
S-waves, or secondary waves, move rock particles perpendicular to the direction of travel. That shearing motion requires a material with rigidity, so S-waves pass through solids but not liquids. Their disappearance at the outer core is one of the key clues that this layer is fluid.
P-waves, or primary waves, compress and expand material in the direction they travel and can move through both solids and liquids. They slow and refract sharply when entering the outer core, producing a distinctive global pattern of arrivals. The resulting P-wave shadow zone helped reveal Earth’s internal layering.
Rayleigh and Love waves are surface-wave types, normally discussed in connection with motion along Earth’s surface rather than transmission through the core. The common mix-up is to choose “surface wave” simply because those waves also do not cross the outer core; in standard seismology, S-wave is the precise answer.