of d/L , in addition to other useful functions such as 2-nd/L and tanh 

 (Zird/L). These functions simplify the solution of wave problems described by 

 the linear theory. 



An example problem illustrating the use of linear wave theory and the 

 tables in Appendix C follows. 



*************** EXAMPLE PROBLEM 1*************** 



GIVEN : A wave with a period T = 10 seconds is propagated shoreward over a 

 uniformly sloping shelf from a depth d = 200 meters (656 feet) to a depth d 

 = 3 meters (9.8 feet). 



FIND: The wave celerities C and lengths L corresponding to depths d = 200 



meters (656 feet) and d = 3 meters (9.8 feet). 

 SOLUTION: 



Using equation (2-8a) , 



L =ll_ = M t2 = 1.56T2 m (5.12T ft) 

 o 2Tr 2ir 



L = 1.56T2 = 1.56(10)2 = 156 ^j (5^2 ft) 

 o 



For d = 200 meters 



d 200 



— = = 1.2821 



L 156 

 o 



From Table C-1 it is seen that for values of 



1->1.0 



O 



L L 

 o 



therefore, 



/ d l\ 



L = L = 156 m (512 ft) deepwater wave, since — > — 



o 

 By equation (2-1) 



L 2 



For d = 3 meters 



L 156 



C = - = 



T T 



156 



C = = 15.6 m/s (51.2 ft/s) 



10 



3 



= 0.0192 



L 156 

 o 



2-11 



