Solution Manual for An Introduction to Sonar Systems Engineering 2nd Edition by Lawrence J. Ziomek

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
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** 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