QUALITATIVE DESCRIPTION OF BOTTOM REVERBERATION 



309 



bottom nearly simultaneously. Thus the reverbera- 

 tion begins and ends very abruptly. The time of on- 

 set of the reverberation equals 2d/c, where d is the 

 depth of the bottom below the projector, and c is the 



SURFACE 



8 W 



Figure 2. Vertical incidence of ping on bottom. 



sound velocity. Evidently, as shown in Figure 2, all 

 portions of the beam do not strike the bottom exactly 

 at the same time so that the duration of the rever- 

 beration does depend somewhat on the beam width. 

 For narrow beams, it is easily shown that the rever- 

 beration duration is given by 



do? 

 Reverberation duration =■ t -\- — , (1) 



4c 



where a is the beam width, shown in Figure 2, and r 

 the ping duration. Thus, with very short pings inci- 

 dent vertically on the bottom, the duration of the 

 reverberation may appreciably exceed the ping dura- 

 tion. 



When the beam is incident on the bottom at some 

 slant angle, all parts of the beam do not strike the 

 bottom at the same time. Consequently the rever- 

 beration does not begin or end quite as sharply 

 as in the previous case, and the reverberation 

 duration is greater than the ping duration. This 

 case is illustrated in the second box of Figure 1. 

 In this situation it is easily shown from Figure 3 that 

 the time of onset and duration of the reverberation 

 are given by 



Time of onset 



= - CSC (. + -). (2) 



Reverberation duration = 



r + 



2ad 



•(, + ^)eot(.-^). (3) 



If the beam is pointed up toward the surface, or is 

 horizontal, surface reverberation will be heard before 



the bottom reverberation begins to come in. With a 

 horizontal beam, different parts of the beam strike 

 the bottom at widely spaced intervals, so that the 

 reverberation lasts a long time. These statements are 

 illustrated in the third and fourth boxes of Figure 1. 

 Of course, the sound beam is not actually confined 

 within a cone; some sound is sent in all directions. 

 However, most sound projectors commonly in use 

 confine all but a small fraction of the emitted and 

 received sound within small angles from the beam 

 axis, so that the simple description of Figure 1 should 

 be a good approximation to the observed phenomena. 

 Figure 4 is an experimental illustration of the quaUta- 

 tive predictions of Figure 1. The data making up 

 Figure 4 were obtained in an area where the water 

 depth was 72 ft. It is noticed that the reverberation 

 recorded with the projector directed vertically down- 

 ward consisted of a single pulse of about the duration 

 of the ping. The reverberation levels recorded with 

 the projector directed 30 degrees down fall on a curve 

 approximating the simple case shown in the second 

 bojc of Figure 1. There is a rapid rise of reverberation, 

 due to bottom scattering, at the time corresponding 

 approximately to the range at which the main beam 

 first strikes the bottom (easily calculated as 35 yd for 

 a half beam width of 6 degrees) and reaching a peak 

 at about the range where the axis of the beam arrives 



SURFACE 



W A 



Figure 3. Slanting incidence of ping on bottom. 



at the bottom (40 yd). The peak is followed by a 

 rapid decay. The case of the horizontal beam is il- 

 lustrated in the bottom curve of Figure 4, and is seen 

 to correspond roughly to the bottom curve in Figure 

 1. The initial reverberation recorded at 40 to 50 yd is 

 received from the bottom on the projector side lobe; 

 this type of reverberation decays rapidly for about 



