Final answer:
The statement that compression/expansion waves can change speed but still travel through the outer core is true. These waves, also known as P-waves, demonstrate how wave speed is affected by material properties such as rigidity and density, and are used to study the Earth's interior during seismic events.
Step-by-step explanation:
Waves that move in a compression/expansion motion are known as compressional or P-waves (primary waves). These waves can change speed as they travel through different materials and they do indeed travel through the Earth's outer core because they are able to pass through liquids, unlike shear or transverse waves (S-waves). The statement that waves that move in a compression/expansion motion, change speed but travel through the outer core, is true.
Seismic waves are a clear example that demonstrates how the characteristics of a medium affect wave speed. Longitudinal or P-waves travel faster in more rigid materials such as granite, whereas they travel slower in less rigid materials like sediments. The difference in travel times of P-waves and S-waves is used to determine the epicenter of earthquakes, and to understand the nature of the Earth's core.
The speed of sound also depends on the rigidity of the medium as well as factors like temperature and density. In general, for the same stiffness, waves propagate faster in a less dense medium. After a compression wave, some molecules move forward temporarily, indicating the passage of the wave through the medium.