SOLUTIONS MANUAL AN INTRODUCTION TO SONAR SYSTEMS ENGINEERING SECOND EDITION LAWRENCE J. ZIOMEK Complete Chapter Solutions Manual are included (Ch 1 to 15).

SOLUTION
MANUAL FOR AN
INTRODUCTION TO
SONAR SYSTEMS
ENGINEERING, 2ND
EDITION BY
LAWRENCE J.
ZIOMEK (ALL
CHAPTERS)

, Chapter 1
SECTION 1.2

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

r r0




2 2
r  r0  2(r r0 )

Since r r , r0 r0 , and r rrˆ , then


r r0 r2  r 02 2r( rˆ• r0 )
 r02
r 1  2  2
2 0
 r r 
r 1 b

r 2
rˆ• r
0 0
where b 2
r  r




1

,1-2 Using Fig. P1-2, show that

u ,

v cos ,

and
w ,

where u , v , and w are dimensionless direction cosines with respect to the X , Y , and Z
axes, respectively.


Z




(r, , )
r



Y




X


Figure P1-2




2

, Z



r sin



(r, , )
r



Y

r sin




X




r r sin

r cos r cos



X X

r
r
u




3