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SECOND
INTRODUCTION
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EDITION Answers
TO
LAWRENCE
SONAR& Study
SYSTEMS
J. ZIOMEK
Guide ENGINEERING
Complete Chapter
SECONDSolutions
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SOLUTIONS MANUAL AN INTRODUCTION TO SONAR SYSTEMS ENGINEERING
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ENGINEERING
MANUAL
| 2026
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SECOND
INTRODUCTION
Questions,
EDITION Answers
TO
LAWRENCE
SONAR& Study
SYSTEMS
J. ZIOMEK
Guide ENGINEERING
Complete Chapter
SECONDSolutions
EDITION
Manual
LAWRENCE
are included
J. ZIOMEK
(Ch 1 to 15).pdf
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Chapter
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Manualanswers.
are included (C
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 0
2 0
r
r
SOLUTIONS MANUAL AN INTRODUCTION TO SONAR SYSTEMS ENGINEERING
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ENGINEERING
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SECOND
INTRODUCTION
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LAWRENCE
SONAR& Study
SYSTEMS
J. ZIOMEK
Guide ENGINEERING
Complete Chapter
SECONDSolutions
EDITION
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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
(r, , )
r
Y
X
Figure P1-2
SOLUTIONS MANUAL AN INTRODUCTION TO SONAR SYSTEMS ENGINEERING
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ENGINEERING
MANUAL
| 2026
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SECOND
INTRODUCTION
Questions,
EDITION Answers
TO
LAWRENCE
SONAR& Study
SYSTEMS
J. ZIOMEK
Guide ENGINEERING
Complete Chapter
SECONDSolutions
EDITION
Manual
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are included
J. ZIOMEK
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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
SOLUTIONS MANUAL AN INTRODUCTION TO SONAR SYSTEMS ENGINEERING
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