Sound Wave Basics
Sound waves are mechanical waves meaning they have to interact with something (like air particles or tissue) to propagate. This is as opposed to say electromagnetic waves like light which can travel is a vacuum.
Sounds is also a longitudinal waves. Longitudinal means that the direction of the vibrations are in the same direction or parallel as that of the propagation (think of a slinky toy for example). They have areas of compressions (higher density particles) and rarefactions (lower density particles) as shown below where each line represents a set of particles.
Transverse waves on the other hand have vibration perpendicular to the direction of propagation. Think of a ripple in the water as a rock is thrown into it or a rope that is being moved up and down. A diagram of a transverse wave is as shown below.
For simplicity we (and many ultrasound texts) will represent sound waves as this sinusoidal type of wave, even though it is not technically correct, because it is an easier visual representation to illustrate many properties. Just keep in mind that sound is a longitudinal wave.