SOLUTIONS MANUAL
AN INTRODUCTION TO
SONAR SYSTEMS ENGINEERING
SECOND EDITION
LAWRENCE J. ZIOMEK
Complete Chapter Solutions Manual
are included (Ch 1 to 15)
** Immediate Download
** Swift Response
** All Chapters included
, 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 = r 2+ r 02− 2r( rˆ• r0 )
r02
= r 1 + 2 − 2
2 0
r r
= r 1+ b
r 2 rˆ• r
where b =
r − 2 r
0 0
1
,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
, 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
AN INTRODUCTION TO
SONAR SYSTEMS ENGINEERING
SECOND EDITION
LAWRENCE J. ZIOMEK
Complete Chapter Solutions Manual
are included (Ch 1 to 15)
** Immediate Download
** Swift Response
** All Chapters included
, 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 = r 2+ r 02− 2r( rˆ• r0 )
r02
= r 1 + 2 − 2
2 0
r r
= r 1+ b
r 2 rˆ• r
where b =
r − 2 r
0 0
1
,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
, 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
