Solutions Manual for An Introduction to Sonar Systems Engineering 2nd Edition by Lawrence J. Ziomek – Chapters 1–15 Worked Solutions & Answers

3/15/2026 SOLUTIONS MANUAL
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for An Introduction
MANUAL for to Sonar
An Introduction
Systems Engineering,
to Sonar Systems
2e byEngineering,
Lawrence J. 2e
ziomek
by Lawrence
Chapter J.
1-15.pdf
ziomek Chapter 1-15.pdf




An Introduction to Sonar Systems Engineering,
2nd Edition — Complete Chapter Solutions
Manual by Lawrence J. Ziomek, Chapters 1–15 |
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SOLUTIONS MANUAL for An Introduction
SOLUTIONS
to SonarMANUAL
Systemsfor
Engineering,
An Introduction
Page
2e1by
oftoLawrence
179
Sonar Systems
J. ziomek
Engineering,
Chapter 1-15.pdf
2e by Lawrence J. ziomek Chapter 1-15.pdf

,3/15/2026 SOLUTIONS MANUAL
SOLUTIONS
for An Introduction
MANUAL for to Sonar
An Introduction
Systems Engineering,
to Sonar Systems
2e byEngineering,
Lawrence J. 2e
ziomek
by Lawrence
Chapter J.
1-15.pdf
ziomek Chapter 1-15.pdf




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




1


SOLUTIONS MANUAL for An Introduction
SOLUTIONS
to SonarMANUAL
Systemsfor
Engineering,
An Introduction
Page
2e2by
oftoLawrence
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Sonar Systems
J. ziomek
Engineering,
Chapter 1-15.pdf
2e by Lawrence J. ziomek Chapter 1-15.pdf

,3/15/2026 SOLUTIONS MANUAL
SOLUTIONS
for An Introduction
MANUAL for to Sonar
An Introduction
Systems Engineering,
to Sonar Systems
2e byEngineering,
Lawrence J. 2e
ziomek
by Lawrence
Chapter J.
1-15.pdf
ziomek Chapter 1-15.pdf




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


SOLUTIONS MANUAL for An Introduction
SOLUTIONS
to SonarMANUAL
Systemsfor
Engineering,
An Introduction
Page
2e3by
oftoLawrence
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Sonar Systems
J. ziomek
Engineering,
Chapter 1-15.pdf
2e by Lawrence J. ziomek Chapter 1-15.pdf

, 3/15/2026 SOLUTIONS MANUAL
SOLUTIONS
for An Introduction
MANUAL for to Sonar
An Introduction
Systems Engineering,
to Sonar Systems
2e byEngineering,
Lawrence J. 2e
ziomek
by Lawrence
Chapter J.
1-15.pdf
ziomek Chapter 1-15.pdf




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
SOLUTIONS
to SonarMANUAL
Systemsfor
Engineering,
An Introduction
Page
2e4by
oftoLawrence
179
Sonar Systems
J. ziomek
Engineering,
Chapter 1-15.pdf
2e by Lawrence J. ziomek Chapter 1-15.pdf