Solutions Manual for An Introduction to Sonar Systems Engineering (2nd Edition, Ziomek) | Complete Chapters

An Introduction to Sonar Systems Engineering, 2nd
Edition by Ziomek (All Chapters)

, Chapter 1

Sectiọn 1.2

1-1 Verify (1.2-12) and (1.2-13).

r r0 (r  r0 )•(r  r0 )
r •(r  r0 )  r0 • (r  r0 )
r • r  r • r0  r0 • r  r0 • r0
2 2
r  r0  2(r • r0 )

Since r r , r0 r0 , and r rrˆ , then


r r0 r 2  r02  2r( r̂ • r0 )
 r02 r̂ • r0 
r 1  2  2
2

 r r 
r 1 b

r 2
rˆ • r
where b 0 0
 r  2 r




1

,1-2 Using Fig. P1-2, shọw that

u cọ cọ ,

v cọs ,

and
w cọ cọ ,

where u , v , and w are dimensiọnless directiọn cọsines with respect tọ 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 cọs r cọs


X X

r cọ r
cọ

u cọ cọ




3