A transverse wave is one where the displacement of the medium in which the wave is travelling is perpendicular to its propagation. A pond ripple is an example of a transverse wave.
A transverse wave cannot be instantiated in gases or through liquids because no mechanism exists to drive motion at right angles to the direction of the wave's propagation. It can occur on a liquid's surface, such as with waves at sea, or through a solid, an example of which is one of the two types of seismic waves.
Waves which cause displacement of a medium parallel to the direction of propagation are called longitudinal waves. Classic examples of longitudinal waves are sound waves and the motion found in a "slinky." Sinusoidal pressure variation is created in air when a single-frequency sound wave is passed through it. These densely and loosely packed regions of air molecules occurring in the direction of the sound wave's propagation are characteristic of a longitudinal wave
Longitudinal waves can occur in solid and liquid media. The properties of both wave types are often utilized effectively in geological surveys. In the Earth's material, both transverse (S wave) and longitudinal (P wave) waves are seismic waves. Data collection from geological studies showing longitudinal-wave penetration of a subsurface region and zero transverse-wave penetration suggests the intrusion of a fluid, such as magma, into that area.