Wave shoaling and the angular frequency is proportional to its local rate of change, Simplifying to one dimension and cross-differentiating it is now easily seen that the above definitions indicate simply that the rate of change of wavenumber is balanced by the convergence of the frequency along a ray; Assuming stationary conditions (formula_27), this implies that wave crests are conserved and the frequency must remain constant along a wave ray as formula_28. As waves enter shallower waters, the decrease in group velocity caused by the reduction in water depth leads to a reduction in wave length formula_29 because the nondispersive shallow water
Shock wave of sound, so that the sound waves leaving the aircraft pile up on one another, similar to a traffic jam on a motorway. When a shock wave forms, the local air pressure increases and then spreads out sideways. Because of this amplification effect, a shock wave can be very intense, more like an explosion when heard at a distance (not coincidentally, since explosions create shock waves). Analogous phenomena are known outside fluid mechanics. For example, particles accelerated beyond the speed of light in a refractive medium (where the speed of light is less than that in a vacuum, such as