440 
Git) prevents the integral #{ from converging as [, ©. However, 
the afterflow term contributes only a slowly varying term of the order of 
ig to Ate If Ren is a time long in comparison with the time of 
decay of the pressure on the surface of the gas sphere but short relative 
to the time of decay of the afterflow term av" le » “ will approach the 
value Gm te 2 © 
K,=—sai | Gat x —— 
m ~ Bae c* Pies P oP," (6.6) 
and remain nearly constant for all distances at which the peak pressure in 
the initial pulse has practical interest. In the peak approximation, Eq. 
4.21 # is of course independent of ¢, and has the value FG MPa, 4° 
at all times, 
We turn now to the time scale of the pressure wave at the point 
R . The parameter Y , Eqs. 5.23 and 6,2, measures the spread of the 
time scale. Waves generated at the gas sphere in the short interval (si 
are spread out over the much longer interval a when they arrive at a 
distant point R - We first consider the asymptotic form for Y appropriate 
to the peak approximation, Eq. 4.21. In this approximation, the second of 
Eqs. 6.2 becomes 
OE al ip ae (6.7) 
In other words, y. is proportional to the reciprocal of the dissipation 
parameter % . As a consequence of Eq. 6.7, we find that the asymptotic 
duration Q of the pulse, equal to 20,/ 2, does not depend directly on the 
time 8 of emission of the wave from the bubble surface, Instead 8 depends 
only on the properties of water and the peak pressure Pm at the sist e 
53 
