SHOCK WAVE is a thin transitive area propagating with supersonic speed in which there is a sharp increase of density, pressure and speeds of substance. Shock waves arise at explosions, detonation, supersonic movements of bodies, powerful electric discharges etc.
Let's consider an object which moves with speed of sound (the plane, for example). At each moment of time it will radiate a circular sound wave. Because the speed of source coincides with speed of sound, emitted waves superpose each other and there is a jump of pressure (front of a shock wave) ahead of source as shown in animation.
If the source moves with speed less than speed of sound, then the shock wave is not generated. Ordinary sound waves propagate forward in the direction of source motion, overtaking it, and back. Due to Doppler effect the still receiver located ahead a source detects a sound with the greater frequency, than emitted. If detector is behind of source, then the received frequency will be lower then emitted. In animation the rings show the surfaces of equal phase in the sound wave generated by a source. We see, that ahead of a source the density of such lines is more than behind of it. Because the speed of sound relatively the media is equal in all directions, the frequency of sound ahead a source and and behind of it will be different.
Let's consider a case when the source of a sound moves in the environment with supersonic speed (in animation the source moves with double speed of sound). In this case sound waves can not overtake a source and for this reason there are no sound waves before a source, they appear only behind of it. Sound waves arising behind a source superpose with each other and form in space a conic surface of high pressure. This surface is a shock wave. It is easy to show, that a sine of the angle formed by front of a shock wave with a direction of movement of a source is equal to the ratio of speed of sound to speed of source (i.e. it is the reciprocal of Mach number).
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