D. FE. Weston 65 
3.9. ACKNOWLEDGMENTS 
Figures 3.3, 3.4 and 3.5 are reproduced fromthe Proceedings of the Physical 
Society published by the Institute of Physics and the Physical Society [10]; and 
Fig. 3.6, from the Geophysical Journal published by the Royal Astronomical 
Society [9]. 
REFERENCES 
1. A.B. Arons, "Secondary Pressure Pulses Due to Gas-Globe Oscillations in Underwater Explosions: 
II. Selection of Adiabatic Parameters in the Theory of Oscillation,” J. Acoust. Soc. Am., Vol. 20, 277- 
282 (1948). 
Be das }Bhs eee "Underwater Explosion Shock Wave Parameters at Large Distances from the Charge," J. 
Acoust. Soc. Am., Vol. 26, 343-346 (1954), 
3. R.H. Cole, Underwater Explosions (Princeton Univ. Press, Princeton, New Jersey, 1948). 
4. C. Herring, "Physics of Sound in the Sea, Part I, Transmission,” NDRC Summary Technical Report, 
Div. 6, Vol. 8 (1946). 
. F, J. McDonal, F. A. Angona, R.L. Mills, R. L. Sengbush, R. G. van Nostrand, and J.E. White, "Attenua- 
tion of Shear and Compressional Waves in Pierre Shale,” Geophysics, Vol. 23, 421-439 (1958). 
. P.N.S, O'Brien, "Seismic Energy from Explosions,” Geophysics, Vol. 3, 29-44 (1960). 
. D. Schofield, "Transducers,” Inst. on Underwater Acoustics (1961). 
. "Underwater Explosion Research," Office of Naval Research, Joint Anglo-American Compendium of 
Reports in three Volumes (1950). 
9. D. E. Weston, "The Low-Frequency Scaling Laws and Source Levels for Underground Explosions and 
other Disturbances," Geophysics, Vol. 3, 191-202 (1960). 
10. D.E. Weston, "Underwater Explosions as Acoustic Sources," Proc. Phys. Soc. (London), Vol. 76, 233- 
249 (1960). 
CONTI O on 
DISCUSSION 
PROFESSOR M. FEDERICI asked whether the change of shape of the shock 
wave, as it progresses, had any influence on the scale law. 
MR. WESTON: The explosion-similarity principle takes account of the main 
changes in the shock-wave shape; but, to proceed from there to the w3 and Ww 
spectrum scaling laws for a fixed range, it is necessary to assume spherical 
spreading. In fact, the peak pressure falls off faster than this (with an extra 
factor of 1.13 in the index) and, at the same time, the shock-wave duration in- 
creases slowly. This necessitates some small corrections to the above laws, 
leading, for example, to a slight increase in the expected dependence of high- 
frequency spectrum level on charge weight. At stillhigher frequencies or at long 
range, there is, in addition, a falling-off in spectrum level due to a lengthening 
of the shock rise time. This last effect is not taken into account in the explosion- 
similarity principle, since the latter implicitly assumes an instantaneous rise. 
PROFESSOR T.S. KORN asked the order of velocity change in the shock wave 
as compared with the normal sound wave and whether the normal laws of dif- 
fraction were applicable. He also inquired if a slow-burning explosive material 
led to some improvement in the over-all efficiency as a source. 
MR. WESTON: Very near the charge, the shock velocity is a few times 
greater than the normal sound velocity; but, at distances of several charge 
radii, it is only fractionally greater. I think that some modifications to normal 
diffraction theory might be necessary. On the second point, the underwater 
acoustic outputs of slow-burning and high explosives are very different. The 
main wave from the former is of rounded form; compare the sharp rise of the 
