MEDSTUDY.COM
SOLUTIONS
MANUAL for An
Introduction to
Sonar Systems
Engineering, 2e
by Lawrence J.
Ziomek
(All Chapters)
,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
r r0 r 2 r 02 2r( rˆ• r0 )
r2
r2 1 02 2 0
r r
r 1 b
r 2 rˆ• r
where b 0 2 0
r
r
1
,MEDSTUDY.COM
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
(r, , )
r
Y
X
Figure P1-2
2
, MEDSTUDY.COM
Z
r sin
(r, , )
r
Y
r sin
X
r r sin
r cos r cos
X X
r cos
cos
r sin
u sin cos cos
3
SOLUTIONS
MANUAL for An
Introduction to
Sonar Systems
Engineering, 2e
by Lawrence J.
Ziomek
(All Chapters)
,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
r r0 r 2 r 02 2r( rˆ• r0 )
r2
r2 1 02 2 0
r r
r 1 b
r 2 rˆ• r
where b 0 2 0
r
r
1
,MEDSTUDY.COM
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
(r, , )
r
Y
X
Figure P1-2
2
, MEDSTUDY.COM
Z
r sin
(r, , )
r
Y
r sin
X
r r sin
r cos r cos
X X
r cos
cos
r sin
u sin cos cos
3
