SOLUTIONS MANUAL for An Introduction to Sonar Systems Engineering, 2e by Lawrence J. Ziomek ||ISBN:9781032190037

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SOLUTIONS
MANUAL for An
Introduction to
M

Sonar Systems
ED

Engineering, 2e
by Lawrence J.
ST

Ziomek
U

(All Chapters)
D
Y

,MEDSTUDY.COM



Chapter 1

Section 1.2

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

r  r0 


2
 r  r0  2(r r0 )
2




Since r  r , r0  r0 , and r  rrˆ , then
M

r  r0  r 2 r 02 2r( rˆ• r0 )
ED
  r2 
 r2 1  02  2 0
 r r 

 r 1 b
ST
 r 2 rˆ• r
where b  0  2 0
 r 
 r
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1-2 Using Fig. P1-2, show that

u  cos  sin cos ,

v  cos   sin sin ,

and
w  cos  cos ,

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


Z
M
ED

(r, , )
r
ST

Y
U
D

X
Y

Figure P1-2




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Z



r sin



(r, , )

r



Y
M
r sin
ED

X
ST

r r sin

r cos r cos
U

X X 
D

r cos
cos 
Y
r sin
u  sin cos  cos




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