Introduction To Sonar Systems
Engineering, 2e By Ziomek (CH 1To 15)
SOLUTION MANUAL
1
, Chapṭer 1
Secṭion 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
r2 2(r r0 )
r0
Since r r , r0 r0 , and r rrˆ , ṭhen
r r0 2
r2 2r( rˆ r )
r 0 0
rˆ r0 ⎞
r 2 ⎜ 1 ⎛ r0
2
2 ⎟
⎝ r ⎠
2
r
= r 1+ b
⎛ rˆ
where r0
r0
b 2 2
⎞ r
⎝⎜
r
⎠⎟
2
,1-2 Using Fig. P1-2, show ṭhaṭ
u cos sin cos ,
v cos sin sin ,
and
w cos cos ,
where u , v , and w are diṃensionless direcṭion cosines wiṭh
respecṭ ṭo ṭhe X , Y , and Z
axes, respecṭively.
Figure P1-2
3
, r cos
cos
r sin
u sin cos cos
4
Engineering, 2e By Ziomek (CH 1To 15)
SOLUTION MANUAL
1
, Chapṭer 1
Secṭion 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
r2 2(r r0 )
r0
Since r r , r0 r0 , and r rrˆ , ṭhen
r r0 2
r2 2r( rˆ r )
r 0 0
rˆ r0 ⎞
r 2 ⎜ 1 ⎛ r0
2
2 ⎟
⎝ r ⎠
2
r
= r 1+ b
⎛ rˆ
where r0
r0
b 2 2
⎞ r
⎝⎜
r
⎠⎟
2
,1-2 Using Fig. P1-2, show ṭhaṭ
u cos sin cos ,
v cos sin sin ,
and
w cos cos ,
where u , v , and w are diṃensionless direcṭion cosines wiṭh
respecṭ ṭo ṭhe X , Y , and Z
axes, respecṭively.
Figure P1-2
3
, r cos
cos
r sin
u sin cos cos
4
