352 
ae 
= 2_ue = eG my. A ; 
Therefore dP = — eae dt Te + uy dr (for eirines)selnallings points in the 
pulse at different times). 
where P = f+ u = 2f = 2u which on substitution in equation (4) gives:— 
hs oa, (ht es dr 
ate <a mat 
The adiabatic relation between pressure p and density p for water is given by:— 
s 
(p + p.)® 
——> = ‘constant 
p 
e c 2 
= ss = By ) 
Whence f f p do Te (c Cy’ 
Po 
where aoe = 3202; Cs velocity of sound in water at atmospneric pressure. 
Substitution of equatian (6) in equation (5) gives 
(less ny = 2. eaehates wench 
c= Cc) ios ee ote 
or after integration 
wri 
= J = 
c (c Cy) M 
where M is constant for corresponding points on the pulse at different times. 
Further, since 
See aa (reici=ee—e (cmc) + c= Att ee 
therefore from equation (7) 
de 
CTR 
1 2 
c (c - ¢,) 
which, after integration, gives 
c 
a Stes pleat gc 
2 HY nti 
“Cy cmt (c ie )2 
° 
c-c¢ 
Substitutes (===> =x. 
t 
° 
x 
2 
& Seal dx 
Then ts ty == J 3 
cae 4 (14 x)mt x? 
2 
whence by writing | ——— =u a(xs) 
x2 (14 xt x? 
t,-t, = 1 (x3) = 4 (x,) 
ries il m2 Si 
c m1 
° 
(4) 
(5) 
(6) 
(7) 
(8) 
IM ceeve 
