If both sides of Equation 2-11 are multiplied by d/L, it becomes: 



d d , /27rd\ 



— = - tanh (2-12) 



The term d/L^ has been tabulated as a function of d/L by Wiegel (1954), 

 and is presented in Appendix C on Table C-1. Table C-2 includes d/L as 

 a function of d/L^ iri addition to other useful functions such as 2ird/L 

 and tanh(2Trd/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 



************** 



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

 over a uniformly sloping shelf from a depth of d = 600 feet to a depth 

 of d = 10 feet. 



FIND : The wave celerities C and lengths L corresponding to depths of 

 d = 600 feet and d = 10 feet. 



SOLUTION: 



Using Equation 2-8, 



L^ = 5.12 T^ = 5.12 (10)^ = 512 feet. 



For d = 600 feet 



d 600 



Lo 512 



1.1719. 



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



d 



->1.0 



K L' 



therefore 



fa. 



L - L^ = 512 feet (deepwater wave, since — > — 



2-1 



