Every sound we hear, every photon of light that hits our eyes, the movement of grass blown by the wind and the regular beat of the tides are all examples of waves. They are all around us.
Movement of the particles are parallel to the motion of the energy. Sound waves moving through the air is an example of this type of wave.
movement of the particles are at right angles (perpendicular) to the motion of the energy. Movement of a wave through a solid object like a stretched rope or a trampoline is an example of this type of wave.
In longitudinal waves, the particle displacement is parallel to the direction of wave propagation. The particles oscillate only back and forth about their equilibrium positions. sound waves are longitudinal waves. The primary wave during earth quake is also longitudinal wave.
In these waves particle displacement is perpendicular to the direction of propagation of the wave. The particles only oscillate up and down about their mean positions as the waves passes. A wave on a rope is a transverse wave. All electromagnetic waves including light is transverse waves. Secondary wave in an earthquake is a transverse wave.