As a geophysicist with expertise in seismology, I can tell you that S-waves, also known as secondary waves or shear waves, cannot travel through the inner core of the Earth. This is because S-waves require a solid medium to propagate; they cannot travel through liquids or gases. The inner core of the Earth is believed to be primarily composed of solid iron and nickel, but the outer core is thought to be in a liquid state. When S-waves encounter the liquid outer core, they are absorbed and do not continue to propagate into the inner core. This property of S-waves provides evidence for the liquid nature of the outer core and the solid nature of the inner core. read more >>

P-waves pass through both mantle and core, but are slowed and refracted at the mantle / core boundary at a depth of 2900 km. S-waves passing from the mantle to the core are absorbed because shear waves cannot be transmitted through liquids. This is evidence that the outer core does not behave like a solid substance.read more >>