What are the wave of muscle contractions that pushes food through digestive system?

The waves of muscle contractions that pushes food through the digestive system are called peristalsis.

Peristalsis is a coordinated, rhythmic contraction of the muscular walls of the digestive tract that propels food through it. It occurs when the circular muscles (which encircle the digestive tube) contract while the longitudinal muscles (which run along the length of the digestive tube) relax. This creates a wave-like motion that moves food forward.

Peristalsis is initiated by the presence of food or fluid in the digestive tract and is controlled by the autonomic nervous system (which operates involuntarily). In humans, peristalsis occurs at a rate of 1-4 cm per second in the large intestine but more rapidly in the stomach and small intestine.