This representation implies that the spectrum of the wave ampli- 
tude is concentrated at one value, T): It also implies that 
the wave record repeats itself every Ty = 8 seconds and that 
the wave amplitude is constant and that therefore equation (3.2) 
holds. 
Now try to match the graph of 7 ,(%) with the actual wave 
record. A point for t to be equal to zero can be chosen at a 
sharply defined crest in the actual wave record. The two records 
will coincide in apparent phase near t = 0, but they will soon 
get out of phase. In addition, the heights of the two wave re- 
cords will rarely coincide. Five sixths of the time the actual 
wave heights will be lower than the heights in the function which 
is supposed to represent the wave record. 
One property which the function which is to represent the 
actual wave record should have is that that function should re- 
present the potential energy of the sea surface averaged over 
time at the point of observation. Thus equation (3.10) should 
hold where T represents a time interval which is long compared 
to the length of a wave group but short compared to the rate at 
which the features of the wave record change (say, twenty minutes). 
{eh eel 
== ( 4 (t))Pdt (3.10) 
ie ial 
Si 
a 
ie 
Obviously this particular method of representing the sea surface 
is an overestimate of the potential energy of the sea surface. 
In addition, many different actual wave records could have the 
Same significant height and period and completely different values 
for the potential energy. 
= BG 
