Chapter 32 



OBSERVED TRANSMISSION THROUGH WAKES 



IN CROSSING A WAKE, sound Undergoes a transmis- 

 sion loss in addition to that resulting from propa- 

 gation through the ocean at large. Transmission loss 

 in the ocean is primarily geometric — the sound 

 beam spreads over large distances because of the 

 inverse square law and because of refraction condi- 

 tions. At frequencies less than 100 kc, the transmis- 

 sion loss from physical causes, such as scattering and 

 absorption, is not very important at the short ranges 

 — a few hundred yards or so — of interest in wake 

 measurements. 



The observed transmission loss in wakes, however, 

 is ascribed exclusively to physical causes, scattering 

 and absorption by air bubbles, because the dimen- 

 sions of wakes are much smaller than the distances 

 over which the geometric effects are particularly im- 

 portant. An exception to this rather sweeping state- 

 ment may have to be made in the case of sound 

 originating in the wake, as described in Section 32.3. 

 These phenomena, however, are little understood at 

 present, as they have not been sufficiently studied. 



32.1 



DEFINITIONS 



The physics of the transmission of sound through 

 wakes has already been fully discussed in Chapter 28. 

 All that is necessary here is to summarize the conven- 

 tions concerning the expression and presentation of 

 the measurements of the transmission loss through 

 wakes. 



The total transmission loss undergone by a sound 

 beam on traversing a wake, or the attenuation, as it is 

 usually called in underwater sound work, is defined 

 by the equation 



H^ = lOlog^, 

 liw) 



(1) 



where 7(0) is the intensity of a parallel beam of 

 underwater sound before entering the wake, and 

 I{w) ig its intensity after it has penetrated the entire 

 width' w of the wake; the transmission loss in the 



wake Hw is distinguished by the subscript w from the 

 transmission loss in the ocean at large, which is com-, 

 monly denoted by the symbol H. According to equa- 

 tion (53) of Chapter 28, the attenuation by the wake 

 can be represented as a product, namely 



H,„ = KeW , (2) 



where w is the geometric width of the wake, usually 

 measured in yards, and Ke is the so-called coefficient 

 of attenuation in decibels per yard. Definitions (1) 

 and (2), as they stand, apply to a sound beam im- 

 pinging perpendicularly upon the wake; for oblique 

 incidence w obviously has to be replaced by w sec /3, 

 where ^ is the angle included between the beam and a 

 line perpendicular to the wake. 



Note that equation (1) may be written in the form 



'liw) 



m 



or, by substitution from equation (2), 



Hw) 



7(0) 



= 10 



-K,u'/10 



(3) 



(4) 



Both Hw and Ke are overall properties of the wake, 

 and it remains to express them as functions of the 

 physical parameters describing the microstructure of 

 the wake, which is known to consist of multitudes of 

 bubbles of all sizes. The acoustic properties of bubbles 

 have been characterized in Chapter 28 by their indi- 

 vidual cross sections as, <Ta, it for scattering, absorp- 

 tion, and extinction of sound, respectively. It will be 

 remembered that these quantities vary considerably 

 according to the size of the bubbles, and that, by and 

 large, only bubbles near resonant size make a signif- 

 icant contribution to the average cross section ap- 

 plying to a population of bubbles of all sizes. 



Should all the bubbles in the wake happen to have 

 exactly the same size, the coefficient of attenuation 

 would be given by [see equation (55) of Chapter 28] 



Ke = —- = 4.34no-e db per cm 



(5) 



5oa 



