1515 
10 
Liebermann”” has recently reported accurately measured 
experimental values of the attenuation coefficient as a function 
of frequency for harmonic waves in sea water, and it is our 
object to apply these results to an analysis of effects one 
might expect to observe in the long range propagation of low 
amplitude shock waves. 
7.2 It should be noted at this point that the object of this 
analysis is not that of determining the so called "thickness of 
a shock front" which many investigators have discussed’. We 
start with the essential result of these investigations, that 
the shock front thickness is vanishingly small at large 
amplitudes, and proceed to investigate the enenee in shape which 
might be expected due to selective attenuation of the higher 
frequency components in accordance with Liebermann's empirical 
data. 
The analysis contains a number of rough approximations 
and is obviously open to criticism on that account, but we feel 
that the present status of knowledge and interest in this field 
does not justify expenditure of the time and effort which a 
more refined theory would require. 
8. The effect of viscosity alone oh a low amplitude exponential shock. 
8.1 The propagation of plane sound waves in a viscous medium 
is governed by the equation? : 
Cy = ct Op uy oF 
ot Ox? 3 Dee (64) 
~ 39 
