Recall that sin(a) = sin(+Tr-a). Thus for a given <f) >_ we get, since a 

 must be obtained from an arcsin relationship, two possible values of 

 wave direction, the true value 6 and its image 





(7.5) 



This is illustrated in Figure 5. In actual practice we do not know the 

 true direction, thus a given value of (j) >_ gives the direction as 



«. = tj* [? * "^J 



where <_ a _< •it/2 is obtained from the principle value of the arcsin. 

 If (j) < 07 then I actually lags J by |(|)| > and Lq = Lq/^Ij < 0. so 

 that arcsin (L^) gives -tt/Z <_ a < 0. 



True Wave 

 Direction 



V 



e' (False Direction) 

 FIGURE 5. DIRECTION ANALYSIS FROM A PAIR OF ARRAY ELEMENTS 



28 



