(c) How far in the direction of wave propagation will a water particle move 

 from its initial position during one wave period when z = 0? 



(d) What is the pressure at the bottom under the wave crest as predicted by 

 both the first- and second-order theories? 



(e) What is the wave energy per unit width of crest predicted by the first- 

 order theory? 



SOLUTION: 



(a) The first-order profile equation (2-10) is 



H 

 n = — cos 6 

 2 



where 



9 = 



2iTx 2irtl 



and the second-order profile equation (2-49) is 



H itH2 cosh(2Trd/L) 



n = — cos 9 H z 



2 8L stnh3(2iTd/L) 



2 + cosh 



Aird 



cos 29 



for 



L 60 



= 0.1 



and from Table C-2 



cosh 



sinh 



cosh 



2Trd ' 



VlTd^ 



4ird 



= 1.2040 



= 0.6705 



= 1.8991 



irH^ co8h(2Trd/L) 

 8L sinh3(2Trd/L) 



2 + cosh 



f4ird' 



= 0.102 m (0.334 ft) 



Therefore , 



n = 0.5 cos 9 + 0.102 cos 2 9 

 Tic 2 = °*^°^ ™ (1.975 ft) 

 Tit, 2 " " 0*398 m (1.306 ft) 



2-38 



