Sound waves are longitudinal mechanical waves. Longitudinal means that the direction of the vibrations are in the same direction 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.
Because sound is a mechanical wave it must have a medium in which to propagate, unlike electromagnetic waves for instance which can propagate within a vacuum.
Transverse waves on the other hand have vibration perpendicular to the direction of propagation 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.