248 



INTRODUCTION 



ocean, and that a steady sound signal is sent out into 

 this ideahzed medium. If we ignore, for the moment, 

 the wave character of sound, and regard a traveling 

 sound impulse as just a steady stream of energy, then 

 each scatterer will return sound energy at a uniform 

 rate, and in a receiver set up to measure the returning 

 sound the reverberation will be heard as a steady 

 ring of constant intensity. It is fairly obvious that in 

 this situation the intensity of the received reverbera- 

 tion should be directly proportional to the intensity 

 of the outgoing signal, since an individual scatterer 

 returns a fixed fraction of the sound energy incident 

 on it. 



If, instead of a continuously projected signal, a very 

 short pulse is put into our ideal mediimi, the resulting 

 received reverberation wiU be quite different in 

 character. Intuitively, we would guess that the re- 

 verberation should gradually taper off to a small 

 value in a few seconds, since by that time the pro- 

 jected energy is already miles away from the re- 

 ceiver. It is not difficult to estimate the rate of decay 

 of reverberation in this simple situation if we ex- 

 pUcitly neglect the absorption of sound energy in the 

 sea. As the sound pulse travels away from the pro- 

 jector, it spreads out over a larger and larger volume; 

 but, if we neglect absorption, the amount of energy 

 included in the pulse does not change. By assuming, 

 as is approximately the case, that the rate at which 

 energy is scattered is simply proportional to the 

 energy in the pulse, it follows that as the pulse travels 

 outward from the source its energy is scattered by 

 the sea volume at a constant rate. However, this 

 scattered sound must make the return trip back to 

 the transducer before it is heard as reverberation; and 

 on this return it is weakened by inverse square 

 spreading. The reverberation from a short pulse, 

 then, is inversely proportional to the square of the 

 range of the scatterers producing it. Since the range 

 is proportional to the time, this means to the man 

 with the earphones that the reverberation decays 

 inversely as the square of the time. 



This result suggests that the intensity of reverbera- 

 tion is a mathematically smooth function of the time, 

 of the sort indicated by the broken line in Figure 1. 

 Such a curve imphes that a short time after the cessa- 

 tion of the projected sound, the intensity of rever- 

 beration is great and that it fades away smoothly and 

 gradually, becoming always fainter and fainter as 

 time goes on. Everyone who has listened to echo 

 ranging knows that this is not the case. The most 

 obvious property of reverberation is its variability, 



its alternation of bursts and silences, as schematically 

 illustrated by the solid line of Figure 1.^ This varia- 

 bility is associated with the phenomenon of inter- 

 ference. 



TYPICAL OBSERVED DECAY 

 ■ HYPOTHETICAL SMOOTH DECAY 



TIME- 



FiGURE 1. Decay of reverberation intensity. 



Interference arises because of the wave-like char- 

 acter of sound. Because of interference, the reverbera- 

 tion from n similar scatterers illuminated by the ping 

 does not always have n times the intensity which 

 would be observed if only one scatterer were present. 

 At a particular instant, the sounds returning from 

 the n scatterers may interfere destructively at the 

 hydrophone so that the n sounds annul one another 

 completely. Or, the n individual sounds may all com- 

 bine constructively, so as to give v? times the in- 

 tensity which would have been due to one of the 

 scatterers alone. These are two extreme cases; but in 

 general the n scatterers together may produce com- 

 posite intensities ranging all the way between these 

 two limits. The resultant intensity that occurs in a 

 given situation depends in a critical way on the 

 exact positions of the scatterers relative to one an- 

 other. Since in the actual ocean the separations of the 

 scatterers change from one portion of the ocean to 

 another, it is plain that the reverberation from a ping 

 should not change smoothly with time; rather, it 

 should change irregularly, with bursts where the 

 interference of the individual tiny echoes is primarily 

 constructive, and relative silences where the inter- 

 ference is primarily destructive. 



There is yet another compHcation. If the echo- 

 ranging ship and the scatterers were all fixed in posi- 

 tion, the pattern of bursts and silences, although com- 

 plex, would not change from one ping to the next. 



