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5.5 It is evident from the preceding discussion that the 
Plane wave approximation fails in two principal respects. 
(a) It does not give a reflected pressure time curve with a 
precursor starting at a finite time prior to arrival of the 
reflected peak as would be expected on the basis of the ray 
picture, but instead shows a precursor starting at -00. This is 
evidence of error in the treatment of the low frequency components. 
(b) Equation (63) shows that in the general spherical case, the 
phase shift at a given “ is a complicated function of ~ instead 
of being independent of © as in the plane wave theory. This 
means that the shapes of reflections based on plane wave theory 
would be somewhat in error even in the neighborhood of the peak, 
where the higher frequency components dominate. That this 
error is not very serious at reasonably large distances from the 
charge is demonstrated by the general agreement between theory 
and experiment in Figures 2 and 3. 
The rigorous calculation of the shape of the 
reflected pulse when an incident exponential is subjected to 
the shifts implied in equation (63) would be an exceedingly diffi- 
cult problem. 
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