Sonar Systems Engineering 2nd Edition – Complete Solutions Manual (Ch. 1–15)

An Introduction to Sonar Systems Engineering,
2nd Edition — Complete Chapter Solutions
Manual by Lawrence J. Ziomek, Chapters 1–15 |
Verified 2025–2026




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Sona r System s Eng inee ring Solutions Manual, La wre nce J. Ziomek 2nd Edit ion, Sonar Eng inee ring Cha pters 1– 15, Sona r Sy stems Study G uide, Engineering Te st Bank, Sonar Sy stems Que stions a nd Answe rs, Engineering Exam Pre p 2025, Sonar Sy stems E ngineering Practice, Sol utions Manual for Sonar Engineering, Sonar E ngineering Exam Rev iew, Sonar S ystem s Enginee ring Study Materia l, Chapter S ol utions 1– 15, Sona r System s Enginee ring Rationale s, Enginee ring Exam Que stions, Sonar Sy stems Engineering 2025 –2026… ………… …

, 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 )
  r02 
 r 1  2  2
2 0
 r r 

 r 1 b

 r 2 rˆ• r
where b  0
2 0
 r 
 r




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