1491 
lost because of the limited high frequency response of the 
recording system. The theoretical peak pressure of the 
reflected wave is infinite since, in equation (18), Pr as t 
——s O. This singularity is associated with the assumption 
of a mathematical discontinuity (perfect shock) in the incident 
pressure wave. For a shock with a finite rise time, the 
reflected peak would be finite. Even in the case of mathematical 
discontinuity treated above, energy conservation is not violated 
since the function Pr is of integrable square as shown in 
Section 2.4. 
The high experimental peaks attest to the effect of the 
steepness of the shock front even though the rise time is 
actually finite. 
The slowly rising precursor which leads the peak of the 
reflection is associated with the propagation of a certain amount 
of energy through the reflecting medium at a velocity higher than 
that of the primary medium. In the plane wave treatment, the 
precursor starts rising at -00 since the plane wave must 
essentially be considered as originating at an infinite distance 
(or time) from the point of observation. For a spherical wave 
originating at a given point source, the precursor would start 
at a finite time before arrival of the reflected peak, the time 
terval being determined by the least time path connecting the 
origin and point of observation. 
3e4 In cases of shallow layer propagation, successive higher 
ay Bees 
