



 where the acceleration due to gravity g is 9.8 m/sec^{2}; L=wavelength
 where the acceleration due to gravity g is 9.8 m/sec^{2} and d=depth
 where tanh is a mathematical function known as the hyperbolic tangent and L=wavelength; here you would need to know the wavelength and depth and have access to hyperbolic tangent tables
where T=period and g=9.8 m/sec^{2} (or 32 ft/sec^{2})  the equation can be simplified to L = 1.56 T^{2} (for meters) or 5.12 T^{2} (for feet)
 deep water waves that have the greatest wavelengths and longest periods, travel the fastest and are the first to arrive in regions distant from the storm which generated them
 if you toss a stone into a pond, a band of ripples is produced  this band gets wider with increasing distance from the original disturbance and the ripples of greater wavelength progressively outdistance those with shorter wavelengths (they outrun the shorter ones)
 this is dispersion (separation of waves by their differing rates of travel) and it produces swells
 progressive groups of swell with the same origin and wavelength are called wave trains
 the leading wave in a train is drained of energy (because it must set up the circular motion), but after the wave train passes, it leaves behind enough energy to generate a new wave
 as a wave advances through the group, each wave moves through the group to die out at the front  the distance traveled by each individual wave as it travels from rear to front of the group is twice that traveled by the group as a whole
 hence the wave speed is 2 x the group speed or the group speed is 1/2 the wave speed
 it is inevitable that swells from different disturbances will run together  when this happens, they will interfere with each other
 when crests of two wave trains coincide, the amplitudes are added (constructive interference)
 when the wave trains are out of phasethe crests coincide with the troughs  the amplitudes cancel out (destructive interference); get mixed interference when crests and troughs do not coincide
 thus, the wave trains interact, lose their individual identities and form a new group of waves separated by regions free from waves
 interaction with the bottom slows the wave, but waves behind this first wave continue at their original speed  thus period remains unchanged while wavelength decreases; the wave then becomes too high for its decreasing wavelength
 depth continues to decrease and the crest of the wave breaks  the turbulent mass of water rushing shoreward after the break is known as surf and the surf zone is that region between the shore and the breaking waves
 there are 4 types of breaking waves:
 spilling breakers  the crest moves forward faster than the wave as a whole; foam eventually covers the leading face of the wave; characteristically found on a gently sloping shoreline
 plunging breakers  the crest curls over and plunges downward with considerable force
 collapsing breakers  similar to plunging breakers, but instead of the crest curling over, it collapses; occur on beaches with moderately steep slopes
 surging breakers  crests remain relatively unbroken as the waves slide up the steep beach


 but if a basin is open at one end, it is possible for a node to occur at the entrance of the basin and an antinode at the landward end; water levels will then rhythmically oscillate between node and antinode and will result in damage on the landward side