2 General Remarks on Waves 



a stable equilibrium: gravity and surface tension. If disturbances of this 

 equilibrium occur, both forces tend to restore the equilibrium. If gravity 

 causes the return to the state of equilibrium, we speak of gravity waves, 

 in contrast to capillary waves, for which surface tension is the restoring 

 force. All large waves in the ocean are gravity waves; only when dealing 

 with the smallest waves of a few centimetres length do we have to take the 

 capillary forces into account (see p. 77). 



In water waves the disturbing motion of the individual particles is per- 

 pendicular to the direction of the wave and, therefore, they belong to a group 

 called "cross waves", in contrast to the "longitudinal waves", where the 

 separate particles oscillate backwards and forwards hi the direction of pro- 

 gress. In the longitudinal waves the elasticity of the medium is the force 

 that tries to bring the particles back to their state of rest. This elasticity 

 causes a succession of increases and decreases of the density of the medium. 

 To these longitudinal waves belong the sound waves, which have shown 

 their importance in oceanography by the utilization of echo sounding. They 

 also play an important part in submarine acoustics. 



Classification of Waves 



We can classify the waves according to the oscillations of the individual 

 particle: (a) in progressive and standing waves, according to the forces which 

 generate and maintain them; (b) in forced and free waves, according to the 

 relation between the velocity of the waves and the depth; (c) in surface or 

 short, or deep water waves and long or shallow water waves. The first class 

 can be subdivided into progressive and standing waves. 



(a) Progressive waves are characterized by the fact that each water particle 

 in a certain level executes the same closed orbit within a definite time. How- 

 ever, all particles do not participate in this motion with the same phase. 

 The phase lags for the particles in the direction of the wave propagation and 

 is dependent upon the wave velocity. The simplest form of a progressive 

 cross-wave is obtained when we subject the individual particles of the surface 

 to displacements according to the law of harmonic oscillations. If we call 

 this displacement r/, we obtain 



2n 

 r\ = A sina = v4 sin— t . (1.1) 



A is the amplitude of the displacement (elongation), 2A is its range, a is 

 the angle determining the time of the displacement (phase angle). T, which 

 is known as the period of oscillation, is the time needed by each particle 

 for a complete oscillation. During this time, a passes through all values 

 from to 2tt; consequently, in a unit time the angle 2ji/T, so that, for any 

 given time t, a becomes {2njT)t and r\ takes the second form of (1. 1). / = 

 determines the time when the movement starts. 



