What are the kinds of waves, and in what materials do they appear?

There are two kinds of waves, longitudinal and transverse. Longitudinal waves are waves that vibrate in the same direction that they travel (propagate). Transverse waves vibrate across their direction of travel.

Every physical material — solid, liquid, and gas — can conduct a longitudinal wave — that’s a compression wave, also known as sound (though often we call it sound only if it’s of a frequency near the range of human hearing) — in any direction. There are no longitudinal waves other than compression, i.e., sound, waves that matter on the MCAT.

Compression waves propagate in all directions through their media (i.e., sound diffuses).

Every physical material with a surface (i.e., every solid object, and every liquid/gas and liquid/liquid interface) can conduct a transverse wave in any direction along the surface, with displacement normal to the surface. Note that a thin wire is a special case, essentially a surface with normals pointing out of the wire in all directions, so it can vibrate in any direction perpendicular to it.

Though there have been MCAT passages with waves traveling in multiple directions on surfaces, these were unusual; in almost all problems, there is only one wave. Waves on surfaces, and especially liquid surfaces, can be very complex to model, so they don’t appear very often.

Other waves are possible, including transverse waves far from the surface of objects. Though these waves might appear, their precise properties shouldn’t matter on the MCAT.

In addition to waves in substances, light can be modeled as a transverse wave. Never mind what it’s a wave of.