where x is measured seaward from the toe of the nearshore slope. 

 By definition 



or defining dx, 



This gives 



g - S 2 (207) 



dx = |£ (208) 



b 2 



dx dd 



c S 2 v^d 



and, for a constant shelf slope, 



-d 



(209) 



2 dd 2(d^. d l/2 3 



Jd 



s U 8 s 2 v^d s 2 »J/? 



Substituting equation (210) into equation (205) gives 



8 ( d 2 /2 " d i /2 ) 



T = l— -| (211) 



n S 2 g^2 



where T is a resonant wave period where the reflected wave and incident 

 wave are ir radians out of phase, and n = 1, 2, 3, . . . Equation (211) 

 provides a first approximation for the resonant wave periods. 



******* 



******* EXAMPLE PROBLEM 15************** 



GIVEN : The water depth, d g , at the toe of a nearshore slope is 30 

 meters. The width of the shelf, l s , is 30,000 meters (18.6 miles) 

 and the water depth, d g , at the the seaward edge of the shelf is 

 60 meters (196.9 feet). 



FIND : The resonant wave periods for the shelf. 



SOLUTION : The slope of the shelf, S 2 , for a constant slope is given by 



d ? - d 60 - 30 



S = — 2. = = 0.001 



2 4, 30,000 



100 



