442 
sharp pressure peak exists immediately at the shock front. If such 
a peak existed at the gas sphere surface during the generation of 
the wave, it would be wiped out by subsequent development of the 
wave, accompanied by destruction of the wave crest and spreading 
of the time scale, 
An important quantity characterizing the wave is the time 
integral I of the pressure, which we may call the impulse. The 
values of I and Py, are useful in characterizing the duration and 
intensity of the initial pulse. We define I as follows, 
tm 
dit = prt at ; (6.10) 
t 
o 
where t is the time of arrival of the wave front at R and t,, = to 
is a finite time long relative to the duration of the initial pulse. 
Due to the afterflow, I fails to converge for ten —~ CO unless the 
oscillations of the gas sphere are taken into account. From the equa- 
tion of propagation, we get 
T 5 faz/R) L, ) 
“a 
te 0 
Ie Ge ee fe 4 (6.11) 
om Va Gv : 5 XE(WA?, 
te % 
With the use of the asymptotic relations, Eqs. 6.2, we obtain, 
: [EA = £oP fo aK. soon 
F\ 
o 
We remark that the momentum integral 1, is asymptotically determined 
55 
