This is the two dimensional equation of non-dispersive wave 

 motion and represents all types of wave motion in which the 

 velocity is constant. The expressions (3.1), (3.2), (3.3) and 



(4.2) are all particular solutions of this equation. 



Since the equation of wave motion is linear, cp, and 92 are 

 any two solutions of (4.3) and A,cp, + A292 ^^ also a solution, 

 A-| and Ap being arbitrary constants. This illustrates the principle 

 of superposition, which states that, when all the relevant equa- 

 tions are linear, we may superpose any number of individual solu- 

 tions to form new functions which are themselves solutions. 



In a dispersive medium, only periodic motions of one discrete 

 period can be considered for simple problems. This is so, because 

 the superposition of several different periods involves a change 

 of shape of the wave form with the distance traveled. Therefore 



(4.3) is valid only when we assume constant depth and one constant 

 period. 



Chapter 2, Refraction 



5, Bases of modern refr action theory 



Wave velocity is a function of depth (h) and period (T), that 

 is 



c = c[h(x,y),T]. (5.1) 



For this to hold in the known refraction problems which were 

 tested in the ripple tank, it was necessary to maintain the period 

 constant. 



In discontinuous, non-dispersive media, the general wave equation 

 is satisfied, the wave equation for each medium taking the form 



10 



