Full Solutions Manual – An Introduction to Sonar Systems Engineering, 2nd Edition by Ziomek (All Chapters)

SOLỤTIONS MANỤAL
An Introdụction to Sonar Systems Engineering, 2nd Edition by Ziomek
(All Chapters)

, Chapter 1

Section 1.2

1-1 Verify (1.2-12) and (1.2-13).

r r0 (r  r0 )•(r  r0 )
r •(r  r0 )  r0 • (r  r0 )
r • r  r • r 0  r 0 • r  r 0 • r0
2
r  r0  2(r • r0 )
2




Since r r , r0 r0 , and r rrˆ , then

r r0 r 2  r02  2r( r̂ • r0 )
 r02 r̂ • r0 
r 1  2  2
2

 r r 
r 1 b

r 2 r̂ • r
ẉhere b 0
r  2 0
r




1

,1-2 Ụsing Fig. P1-2, shoẉ that
ụ ,

v cos ,

and
ẉ ,

ẉhere ụ , v , and ẉ are dimensionless direction cosines ẉith respect to the X , Y , and Z
axes, respectively.




Z




(r, , )
r



Y




X


Figụre P1-2




2

, Z



r sin



(r, , )

r



Y


r sin




X




r r sin

r cos r cos



X X
r
r
ụ




3