Final answer:
The slowest type of earthquake waves are the surface waves, which travel slower than both P-waves and S-waves and cause the most damage during earthquakes.
Step-by-step explanation:
Among the types of earthquake waves, the ones that travel with the slowest velocity are the surface waves. These waves are similar to surface waves on water and travel slower than waves that move through the body of the Earth, such as P-waves and S-waves. P-waves, or pressure waves, are longitudinal and can travel through solids, liquids, and gases, exhibiting speeds of 4 to 7 km/s. S-waves, or shear waves, are transverse and can only travel through solids, with speeds ranging from 2 to 5 km/s. However, it is the surface waves that ultimately travel slower and are responsible for most of the damage during an earthquake as they move along the Earth's exterior.