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 calculate the form and stability of periodic travelling wave solutions of partial differential equations, and the regions of parameter space in which waves exist and in which they are stable. Examples of phenomena resembling periodic travelling waves that have been found empirically include the following. Periodic travelling wave In mathematics a periodic travelling wave (or wavetrain) is a periodic function of one-dimensional space that moves with constant speed. Consequently it is a special type of spatiotemporal oscillation that is a periodic function of both space and time. Periodic travelling waves play a fundamental role in many mathematical equations, including self-oscillatory