General Remarks on Waves 15 



When the water is deep (short waves), the ratio between the group velocity 

 and the wave velocity is \ ; this ratio increases with decreasing water depth, 

 and becomes equal to 1, when the depth is small in proportion to the wave 

 length (long waves). In many natural phenomena dealing with superposed 

 wave trains, the group velocity is undoubtedly of more importance than 

 the velocity of separate waves, which can seldom be observed independently 

 of each other. What shows is the group velocity of the wave train, and in 

 many cases discrepancies between observation and theory are attributable 

 to confusion of the two quantities. 



Equation (1. 11) is commonly derived from the interference of two wave 

 systems of the same amplitude and of a slightly different wave length; this, 

 however, should not be interpreted to the effect that the group velocity only 

 has any significance in case there are such interferences. According to its 

 intrinsic nature, it is much more general. For general deductions see Rossby 

 (1945, p. 187) and Munk (1947). 



