Solution Manual - An Introduction to Sonar Systems Engineering 2nd Edition by Lawrence J. Ziomek, All Chapters

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Solution Manual

An Introduction to Sonar Systems Engineering

by Lawrence J. Ziomek
2nd Edition
N
U
R
SE
TE
ST

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Chapter 1

Section 1.2

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

r − r0 =
=
=
N
2
=
2
r + r0 − 2(r r0 )
U
Since r = r , r0 = r0 , and r = rrˆ , then


r − r0 = r 2+ r 02− 2r( rˆ• r0 )
R
 r02
= r 1 + 2 − 2
2 0
 r r 
SE
= r 1+ b

 r 2 rˆ• r
where b =
 r  − 2 r
0 0
TE
ST


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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
N
axes, respectively.
U
Z
R
SE
(r, , )
r



Y
TE
ST
X


Figure P1-2




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Z



r sin



(r, , )

r
N
Y
U
r sin
R

X
SE

r r sin
TE
r cos r cos



X X
ST
r cos
cos =
r sin
u = sin cos = cos




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