488 
curve is a good approximation to the initial portions of the experimentally 
obtained pressure-time curves of underwater shock waves from explosive 
sources. It is not, however, a good representation of the latter portions 
of the experimental curve. In the later portions of the curve, the decay 
is much slower than that predicted for an eeioneatiel wave, the tail of 
the wave being the result of essentially incompressive motion exterior to 
the gas surface. The excess pressure associated with this motion becomes 
zero only at that time at which the gas pressure becomes equal to the hydro- 
static pressure. This time is of the order of one-tenth of the period of 
pulsation of the gas bubble and is many times the time constant of the ini- 
tial high-pressure portion of the wave. However, the peak approximation to 
the pressure.time curve provides a good representation of that portion of 
the wave for which the pressure is appreciable. In Figure 10.1, the exper- 
imental vressure-time curve obtained at 20 feet from a 300-lb. charge of 
tyT37/ is compared with the exponential pressure-time curves predicted 
by theory. It is evident that the exponential approximation is a good rep- 
resentation of the initial part of the curve. 
Although the comparison of theoretical and experimental values of 
shock-wave peak pressure is unambiguous, a difficulty arises in the compari- 
son of parameters which result from the integration of the pressure-time 
curve, The experimental form of the shock wave is such that the impulse, I, 
the integral under the pressure-time curve, does not converge rapidly to a 
limiting value with increasing values of the time. It is not therefore 
practical to define an upper limit of the time for which the impulse is 
37/ RewHeColemlocwmcite, ipsiasie. 
98 
