1527 
This approximation has the effect of subjecting 
frequencies higher than 30 or 40 kilocycles to too severe an 
attenuation, but since in any case the very high frequency 
components rapidly cease to contribute appreciably to the pulses 
in wrich we are interested, the approximation is probably 
justified. 
Using equations (95) and (96) together with the numer- 
ical values of A, B, and @ » and converting to ft., sec. wits, 
we obtain: 
3 
a = 7.11 (10-8) x (97) 
Liebermann argues convincingly that all the attenuation 
in underwater sound propagation is ascribable to viscosity, 
thermal conduction effects being negligible. Thus, if finite 
amplitude effects are entirely neglected, one can use estimates 
of a based on (97) together with the known A of the shock wave 
under consideration, to predict rise times and wave shapes for 
various distances * by use of equations (91) and (93). 
9. Correction of the preceding theory for certain finite amplitude 
effects. 
9.1 The theory developed in the preceding section treated the 
effect of viscous attenuation on purely acoustic pressure waves 
and completely neglected the effect of finite amplitude in 
modifying the shape of the wave. Finite amplitude modifications 
enter our problem in two principal aspects: (a) spread of the 
profile (b) "sharpening effect" at the front. 
