Physics of the Sound Barrier        A  sound wave is a compression wave that propagates through periods of high pressure and low pressure. The distance between each high pressure zone is the wave length. When an object moves through the air it pushes the air out in front of it creating these sonic pressure waves, to a certain point. There is a finite speed that sound can move through objects, for example, in air sound travels at 343 m/s. That is what we refer to as the speed of sound(c) or Mach 1. As objects start to approach the speed of sound the air is not able to get pushed out in front of the object before the object passes through that space. This is known as the sound barrier. When an object breaks the sound barrier there is a loud boom, called the sonic boom, that is the result of the air not being able to move out of the objects way and therefore forming a dense cone of air around the speeding object. http://www.audioholics.com/room-acoustics/bass-the-physical-sensation-of-sound The two most common paces that we deal with items breaking the sound barrier are bullets and airplanes. The bullet to the right shows a good example of air being pushed from out in front of its path. The dark line in front of the bullet and spreading out to the sides is the cone of dense air. The turbulent air behind the bullet is the drag from the air trying to fill the vacuum behind the bullet. We can calculate the angle that the dense air shocks that are created with the speed of the bullet due to the following relationship. sin θ =  c v   The sin of the angle is equal to the velocity of the speed of sound divided by the velocity of the object. This shows us that as v becomes greater then the angle will have to decrease and become closer and closer to being parallel with the object. The other place that we see the sound barrier being broken is in planes. The fighter jet on the far right has just broken the sound barrier and the white cloud is the shock generated by the dense air. The speed of such planes is often categorized as a mach number. The mach number is the number of times faster then the speed of sound an object is going following this relationship. M =  v c M is the mach number and c is the speed of sound. So if your velocity(v) was twice the speed of sound we would say you were traveling at mach 2, a velocity of half the speed of sound would be mach .5. https://www.nasa.gov/audience/forstudents/5-8/features/what-is-supersonic-flight-58.html http://whnt.com/2016/01/28/navy-jet-breaks-the-sound-barrier-causes-sonic-booms-on-east-coast/