Shock wave cannot travel any further upstream and the pressure progressively builds in that region; a high pressure shock wave rapidly forms. Shock waves are not conventional sound waves; a shock wave takes the form of a very sharp change in the gas properties. Shock waves in air are heard as a loud "crack" or "snap" noise. Over longer distances, a shock wave can change from a nonlinear wave into a linear wave, degenerating into a conventional sound wave as it heats the air and loses energy. The sound wave is heard as the familiar "thud" or "thump" of a sonic boom,
Periodic travelling wave wave speeds. For partial differential equations, periodic travelling waves typically occur for a continuous range of wave speeds. An important question is whether a periodic travelling wave is stable or unstable as a solution of the original mathematical system. For partial differential equations, it is typical that the wave family subdivides into stable and unstable parts. For unstable periodic travelling waves, an important subsidiary question is whether they are absolutely or convectively unstable, meaning that there are or are not stationary growing linear modes. This issue has only been resolved for a few partial differential equations. A number of mechanisms