Name 2 kinds of longitudinal waves and explain how you know they are longitudinal

In a longitudinal wave the particle displacement is parallel to the direction of wave propagation. The animation at right shows a one-dimensional longitudinal plane wave propagating down a tube. The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.The second animation at right shows the difference between the oscillatory motion of individual particles and the propagation of the wave through the medium. The animation also identifies the regions of compression and rarefaction.The P Waves(primary waves) in an earthquake are examples of Longitudinal waves. The P waves travel with the fastest velocity and are the first to arrive. 

Reference: http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html

All the Best :D