438 
The afterflow term gl er negligible relative to the first term at large 
distances for a long period of time after passage of the wave front. In 
fact, we may define the initial pulse as the region behind the wave front in 
which pl Re is negligible. It becomes the dominant term in the afterflow 
region which does not concern us here, 
The asymptotic expressions for the dissipation and spreading 
parameters, A and Y » at large distances are the following, 
“(PoCala)”* (« K fog Ra, )v? 
Pg % Bie. (6.2) 
Gtr) 
de = &p cz tog R/a., ’ 
if we approximate K by unity, from which it differs only slightly. The peak 
Wy 
pressure at the shock front Pin is given by the asymptotic formula 
y (CaS 1/2, i pa 
in = (G*) ae te, R/a,/ - zs 
Eqs. 6.2 and 6,3 have several interesting features. The peak pressure does 
not decrease exactly as / i? as required by the elementary acoustical approx- 
imation, but slightly more rapidly because of the logarithmic factor, 
(log R/a, a Ve in x. This factor varies, of course, very slowly in com- 
parison with 1/fR e its presence is due to the progressive destruction of the 
head of the wave at the shock front (increase of % ) which persists even at 
large distances. The difference between local sound velocity and waveefront 
velocity, which gives rise to destruction of the wave front, is connected 
in an interesting way with the energy dissipation at the shock front, as we 
shall presently see, 
ae 
