A characteristic of all waves is that they transfer energy from one place to another.
Waves, both transverse and longitudinal, typically do not displace the medium very far.
Drop a pebble in a pond. The result is a transverse wave that spreads outward from where the pebble landed, but all the water molecules are doing is bobbing up and down, going nowhere fast.
Shout to your friend all the way across a soccer field. The result is a longitudinal wave that spreads outward from you. The air molecules push each other around roughly in the same direction as the wave's travel, but eventually they all get pushed back around to the same place they were before.
The medium moves at right angles to the direction of motion of a transverse wave. The medium moves in the same direction as the direction of motion of a longitudinal wave.
For a longitudinal wave, the medium has changes in density due to the back-and-forth motion of its molecules. The less dense regions are called rarefactions as the more dense regions are called compressions. This phenomena doesn't happen for transverse waves.
Taking all the above into account, the correct answer is Choice A.
