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TRANSMISSION OF EXPLOSIVE SOUND IN THE SEA 



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ANGLE AT WHICH RAY CROSSES AXIS 



OF SOUND CHANNEL, IN DEGREES 



TYPE I-UNREFLECTED RAYS 



TYPE E- SURFACE REFLECTION AND UPWARD REFRACTION 



TYPE lE-BOTTOM-REFLECTEO RAYS 



HORIZONTAL RANGE TRAVERSED BY RAY IN EXECUTING 



ONE COMPLETE CYCLE OF ITS VERTICAL OSCILLATION 



MEAN HORIZONTAL VELOCITY EQUAL TO ABOVE RANGE 



DIVIDED BY TIME REQUIRED FOR ONE CYCLE 



Figure 18. Mean horizontal velocity and range per 

 cycle for rays oscillating about a sound channel. 



not be true. In any case, however, whether source 

 and receiver are on the axis of the sound channel or 

 not, the number of different rays connecting them 

 increases with increasing horizontal range. The num- 

 ber of such rays decreases, however, with increasing 

 distance of source or receiver from the axis. If either 

 source or receiver is too far from the axis of the sound 

 channel, no ray can get from source to receiver with- 

 out reflection from the surface or the bottom. 



To study these phenomena quantitatively, and to 

 compute times of arrival for the various rays, curves 

 like those shown in Figure 18 are verj^ helpful. What- 

 ever its point of origin, any ray which traverses the 



sound channel can be characterized by the angle at 

 which it crosses the axis of the sound channel; any 

 two rays which cross the axis at the same angle must 

 be congruent, differing only by a horizontal displace- 

 ment. Figure 18 shows how the horizontal range per 

 cycle and the mean horizontal velocity, that is, the 

 quotient of horizontal range per cycle by time per 

 cycle, depend upon the angle of crossing the axis. 



For angles less than a certain critical value, equal 

 to 12.2 degrees in the example shown, the ray 

 oscillates up and down without reaching either the 

 surface or the bottom. For rays of this type (type I 

 in Figure 17) it will be seen that the mean horizontal 

 velocity is least for the axial ray and increases as the 

 angle with the horizontal, and hence the range per 

 cycle, increases. The consequences of this are espe- 

 cially interesting when both source and receiver are 

 on the axis of the sound channel. For this case the 

 first impulse to arrive will come along a ray for which 

 the number of oscillations in depth has the smallest 

 value consistent with avoidance of surface and bot- 

 tom reflections. When the range is small, this ray 

 will have only one half-cycle between source and re- 

 ceiver, but with increasing range more and more half- 

 cycles are required, since the range per complete cycle 

 can never be greater than a certain value, equal to 

 85jkyd in Figure 18. Rays with more and more 

 oscillations will arrive later and later, and if for the 

 moment we ignore reflected rays, the last one to 

 arrive will be the straight axial ray. Thus, the early 

 arrivals will be separated by considerable intervals 

 of time, but later arrivals will be closer and closer to- 

 gether, finally merging into an unresolvable cre- 

 scendo, followed, if we neglect reflected rays, by a 

 sudden silence. Figure 19A shows the times of arrival 

 of these sound channel rays, as computed from the 

 data in Figure 18 for a particular value of the range. 



The total time between the first and last of these 

 arrivals can be computed from the spread in mean 

 horizontal velocities for the sound channel rays; for 

 the case plotted in Figure 18 the total time in seconds 

 comes out to be 0.012 times the range in miles. 



It will be noticed that the early arrivals in Figure 

 19A come in groups of three. The explanation of this 

 is shown schematically in Figure 20 for the simplest 

 case of the first arrivals at a very short range. Each 

 oscillating ray travels much farther in a lower half- 

 cycle than in an upper one; consequently the mean 

 horizontal velocity of a ray between source and re- 

 ceiver will be principally a function of the amplitude 

 of its lower half -cycles which in turn is principally 



