Final answer:
Seismographs are instruments that detect P-waves but not S-waves from an earthquake on the other side of Earth, indicating that S-waves cannot pass through the liquid outer core.
Step-by-step explanation:
The instrument that records P-waves but no S-waves and thus indicates that an earthquake occurred on the other side of Earth is a seismograph. S-waves, being transverse or shear waves, cannot travel through Earth's liquid outer core, which creates an S-wave shadow zone on the opposite side of the planet from the earthquake's epicenter. P-waves, also known as compression waves or pressure waves, can travel through both solid and liquid layers of the Earth. This difference in the ability of P-waves but not S-waves to travel through liquid is key to understanding the internal structure of Earth, as it suggests the existence of a liquid outer core surrounding a solid inner core.