Wind wave may be written as: where C is speed (in meters per second), g is the acceleration due to gravity, and d is the depth of the water (in meters). The period of a wave remains unchanged regardless of the depth of water through which it is moving. As deep-water waves enter the shallows and feel the bottom, however, their speed is reduced and their crests "bunch up," so their wavelength shortens. As waves travel from deep to shallow water, their shape alters (wave height increases, speed decreases, and length decreases as wave orbits become asymmetrical). This process is called shoaling.
Acoustic wave equation include acoustic wave equations that incorporate fractional derivative terms, see also the acoustic attenuation article or the survey paper. The wave equation describing sound in one dimension (position formula_3) is where formula_1 is the acoustic pressure (the local deviation from the ambient pressure), and where formula_6 is the speed of sound. Provided that the speed formula_6 is a constant, not dependent on frequency (the dispersionless case), then the most general solution is where formula_9 and formula_10 are any two twice-differentiable functions. This may be pictured as the superposition of two waveforms of arbitrary profile, one (formula_9) travelling up the x-axis