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
Acoustic wave wave becomes a travelling wave moving rightwards, for formula_14 the wave becomes a travelling wave moving leftwards. A standing wave can be obtained by formula_15. In a travelling wave pressure and particle velocity are in phase, which means the phase angle between the two quantities is zero. This can be easily proven using the ideal gas law where Consider a volume formula_18. As an acoustic wave propagates through the volume, adiabatic compression and decompression occurs. For adiabatic change the following relation between volume formula_18 of a parcel of fluid and pressure formula_2 holds where As a sound wave propagates through