FIND : 



(a) The primary and secondary periods of oscillation, and 



(b) the relative wave height of the wave at a distance one wavelength 

 from the shoreline in relation to the wave height at the shoreline, for 

 the second mode. 



SOLUTION : 



(a) d = 30 meters and a = 12,430 meters 



*■ s 



From equation (189) 



a 



3.2417 



/g^ 



T, = 3.2417 12,43 ° - = 2,350 seconds (39.2 minutes) 

 /9. 807(30) 



From equation (190) 



a 



T 2 = 1.9254 



/gd 

 6 s 



T 2 = 1.9254 12,430 _ _ 1395 secon d s (23.3 minutes) 

 /9. 807(30) 



(b) Both the first and second modes of oscillation are in the range 

 of tsunami periods which are likely to occur. Taking h s as the wave 

 height at the shoreline, Table 1 gives, for the second mode, a height 

 equal to 0.7818 hg where x/a = 2.4 or where x = 2.4 (12,430) = 29,800 

 meters (18.5 miles). The values in Table 1 and Figure 32 show that 

 this is approximately the distance between second-mode wave crests (one 

 wavelength) . 



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



************* EXAMPLE PROBLEM 13 



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



GIVEN : The water depth, d g , at the toe of a nearshore slope is 15 

 meters; the distance a = 621 meters (2,039 feet). Complete reflection 

 occurs at the nearshore slope. 



FIND : The primary and secondary periods of oscillation. 



94 



