196 



TRANSMISSION OF EXPLOSIVE SOUND IN THE SEA 



explosive pulse is subject to the same frequency-de- 

 pendent attenuation law as has been observed for 

 supersonic sound (see Section 5.2.2). A more precise 

 comparison of theory with observation would, how- 

 ever, require knowledge not only of the exact response 

 of the hydrophone and recording system to a dis- 

 continuous change of pressure, but also of the slight 

 dependence of the sound velocity on frequency. The 

 WHOI data, on the other hand, are much less under- 

 standable. The increase in recorded time of rise from 

 13 jusec at short ranges to 50 ^sec at 100 ft implies an 

 attenuation of the high-frequency components of the 

 explosive pulse, which is orders of magnitude greater 

 than that encountered for supersonic sound. The 

 comparative slowness of the increase in time of rise 

 at greater ranges shows that this attenuation is non- 

 linear; and the most plausible suggestion seems to be 

 that it has its origin in the coating of the hydrophone, 

 rather than in the sea water (see Section 8.3). 



So far we have considered only the direct pulse. 

 The surface-reflected pulse may be expected to have 

 a longer time of rise, or more correctly, time of fall, 

 because of the diversity of possible paths from ex- 

 plosion to hydrophone involving reflection from vari- 

 ous wave troughs. Whether the smearing out of the 

 wave due to this effect exceeds that responsible for 

 the time of rise of the direct wave will of course de- 

 pend upon the geometry and especially upon the 

 roughness of the sea. Some typical oscillograms of 

 shots made in an average calm sea are shown in 

 Figure 1, taken from a report by UCDWR^ and 

 from reference 8. These shots show that the rough- 

 ness of the surface has surprisingly little effect on the 

 first part of the reflected pulse, although the tail 

 shows irregularities which are probably due in part 

 to nonspecular reflection. The most remarkable thing 

 about these records, however, is that as grazing inci- 

 dence is approached the effective reflection coefficient 

 of the surface remains close to unity far beyond the 

 point at which the crests of the waves are in the 

 geometric shadow created by the troughs. Figure 2 

 shows the variation of the reflected amplitude with 

 angle of incidence. This quantity was estimated for 

 a number of shots, including those shown in Figure 1, 

 by taking the difference between the reflected peak 

 and the estimated pressure in the direct pulse at the 

 same time. For comparison, it may be noted that for 

 a train of surface waves traveling in the direction 

 from source to receiver, half of the surface of the sea 

 in the region where reflection occurs would be in 

 geometric shadow from source or receiver, or both. 



if the ratio of crest-to-trough amplitude to wave- 

 length is about one-third the angle which the incident 

 ray makes with the horizontal. Since the sea was not 

 unusually calm on the day the shots were made, 

 Figure 2 strongly suggests that the sea surface acts as 

 a flat reflecting plane for supersonic sound even when 

 only the wave troughs are in the direct sound field. 

 An effect of this sort has been predicted theoretically 

 for the case of sinusoidal sound.'" 



1.6 



1.2 



1.0 



c 0.6 



0.2 



0.02 0.04 0.06 0.08 



ANGLE BETWEEN INCIDENT RAY AND HORIZONTAL IN RADIANS 



Figure 2. Variation of peak amplitude of surface- 

 refleeted pulse with angle of incidence. Horizontal 

 range, 1,100 yds; depth of hydrophone, 11 ft. 



Measurements of the time interval between the 

 direct and surface-reflected pulses have been re- 

 ported in a memorandum by UCDWR" and in 

 reference 9, and agree with the values calculated from 

 the geometrical formula (31) of Section 8.7 to within 

 the accuracy of measurement of the depths of cap 

 and receiver. 



In the absence of refraction, one would expect the 

 peak pressure of an explosive pulse having a time 

 constant d to be attenuated at long ranges at approxi- 

 mately the same rate as sinusoidal sound of a suitably 

 chosen frequency, this "effective frequency" being 

 probably a few times smaller than I/O. A detailed 

 relationship between the attenuation of a weak ex- 

 plosive pulse and that of sinusoidal sound could be 

 worked out by the methods of Fourier analysis; how- 

 ever, such a relationship would be considerably af- 

 fected by dispersion, that is, by any variation of the 

 velocity of sound with frequency. This is a phenome- 

 non which must occur if there is a frequency-de- 

 pendent attenuation. A brief discussion of attenua- 



