The rumbling sounds occur during the digestive process. Your tummy grumbles when food is squeezed back and forth through the digestive tract until it dissolves. Foods high in fiber take longer to dissolve, hence grumbles are more frequent. As the body gets used to breaking down higher amounts of fiber, it will increase production of digestive enzymes that help speed the process.
To avoid these embarrassing sounds, add a tablespoon of olive oil to your meals. The fatty acids in the oil relax intestinal muscles enough to reduce rumbling.