Final answer:
The particles in a longitudinal wave vibrate back and forth, transverse waves in a spring are produced by shaking the spring side to side, surface waves in the ocean involve air and water as the two mediums, and mechanical waves require a medium to travel.
Step-by-step explanation:
The particles of a longitudinal wave vibrate back and forth parallel to the direction in which the wave travels. This can be demonstrated using a slinky by properly pushing and pulling it along its length. To produce a transverse wave in a spring, you would move one end of the spring up and down, thus creating disturbances perpendicular to the direction of the wave. This wave movement in the spring would occur if option (c), shaking the spring side to side, is applied to the spring while it is laying on a flat surface. The surface wave that forms when an ocean wave enters shallow water involves two mediums: air and water. Lastly, the type of wave that requires a medium to travel is a mechanical wave, which includes transverse, longitudinal, and surface waves, as opposed to electromagnetic waves that can propagate even in a vacuum.