You might think of a wave at a beach. You can make a ripple of water in a bath tub.
If you have a toy ship, just float it on the surface of water. When you put your hand in and out of water repeatedly, it causes waves. The toy ship also goes up and down. However, the ship will probably not ride the wave and move away.
If you have a rope, grab one end and snap quickly to create a “pulse.” Then, you will see its movement from your end towards the other end. In this case, each part of the rope does not move at the same speed from one end to the other. Instead, it only looks a bump of the rope travels from one end to the other. In fact, each part of the rope just moves slightly up and down when the bump passes by.
When you swing the same end of the rope up and down repeatedly, we can observe “waves” moving from your end to the other end. Many waves are created and move constantly. However, again, each part of the rope is swung up and down around the same position and does not move along the length of the rope. When directions of the displacement and the wave movement are perpendicular, it is called “transverse wave.”
If there is a series of waves, a source of vibration exists somewhere, which causes the waves, and there should also be a medium, which transmits the waves. When you strike a turning fork, it produces a sound wave. In this case, the tuning fork is the source of vibration. Therefore, it is also called sound source. The medium, in this case, is the air. A sound wave also travels in the water, which is now the medium.
Let think of the air as the medium, again. The air is heavy, and it has a mass. In addition, the air has elasticity, like a spring. When you fill a syringe with the air and trap the air in it, you might feel an elastic force. A sound wave in the air travels due to the elasticity, which repeatedly creates “compression” and “rarefaction” of the air. Let us consider the air as a set of particles, the compression of the air can be viewed as air particles are distributed with high density. Likewise, the rarefaction of the air can be viewed as air particles are distributed with low density. Because directions of the displacement of air particles and the wave movement are the same, the sound wave is called “longitudinal wave.”