TEST BANK__An Introduction to Sonar Systems Engineering 2nd Edition by Lawrence J. Ziomek , ISBN: 9781032190037 |All Chapters Included| Guide A+

SOLUTIONS MANUAL
An Introduction to Sonar Systems Engineering

Lawrence J. Ziomek

2nd Edition
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,Table of Contents
1. Introduction to Sonar Systems
2. Fundamentals of Acoustics
3. Sound Propagation in the Ocean
4. Underwater Ambient Noise
5. Sonar Equations
6. Active Sonar Systems
7. Passive Sonar Systems
8. Transducers and Arrays
9. Beamforming and Array Processing
10.Signal Processing for Sonar
11.Detection Theory
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12.Target Strength and Scattering
13.Reverberation
14.Environmental Effects on Sonar Performance
15.Sonar System Design and Analysis
16.Performance Prediction and Evaluation
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17.Special Topics in Sonar Systems Engineering
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, 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
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r − r0 = r 2+ r 02− 2r( rˆ• r0 )

 r02
= r 1 + 2 − 2
2 0
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 r r 
= r 1+ b
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 r 2 rˆ• r
where b = 0
 r  − 2 r
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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
axes, respectively.


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(r, , )
r
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X


Figure P1-2




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