504 



OBSERVED TRANSMISSION THROUGH WAKES 



H — 



or Z, = -^ = 396.8n(re db per yd , (6) 



w 



where Ce in square centimeters is the extinction cross 

 section of this particular size of bubble and n in cm~' 

 is the average number of bubbles of this size per 

 cubic centimeter in the wake, as defined by equa- 

 tion (54) of Chapter 28. In the more realistic case of 

 bubbles of many sizes, the attenuation coefficient is 

 given by equation (67) of Chapter 28, 



Ke = ^ = 1.4 X lO'uiRr) db per yd , 

 w 



(7) 



where u{R)dR is the total volume of air contributed 

 by bubbles with radii between R and i^ + dfl in 1 cu 

 cm of the air-water mixture, or rather the average of 

 this quantity taken over the entire column in which 

 the sound beam and the wake intersect; Rr in equa- 

 tion (7) is the radius of the resonant bubbles cor- 

 responding to the sound frequency used in deter- 

 mining Hy,. 



The total attenuation corresponding to equation 



(5) is 



//„, = 4.34cr,nw = ^M<7eN{w) , (8) 



where N{w) = nw denotes the total number of 

 bubbles in a column of unit cross section. Thus N{w) 

 is a measure of the total bubble population affecting 

 the sound beam. 



Differentiating equation (8) logarithmically with 

 respect to the time, the decay of the transmission loss 

 across the wake is obtained. 



1 



dHy, 

 dt 



1 dN(,w) 



(9) 



H^ dt N{w) dt 



At first, dN{w)/dt perhaps will be positive for suf- 

 ficiently small bubbles, whose number might be in- 

 creased rapidly by the gradual dissolution of bubbles 

 of originally larger size. But ultimately, dN{w)/dt 

 must become negative. It is seen then that the decay 

 rate of the transmission loss affords a direct measure 

 of the rate of disintegration of the bubble population. 



32.2 



EXPERIMENTAL PROCEDURES 



In principle, the experimental determination of the 

 transmission loss through the wake requires only 

 relative measurements of sound intensities. If over 

 the period of observations the range from transducer 

 to hydrophone, and the transducer output and hydro- 

 phone sensitivity remain constant, then the absolute 

 values of any of these three quantities does not have 



to be known; the difference of sound levels recorded 

 by the hydrophone before and after the wake has 

 been laid across the sound beam is simply the trans- 

 mission loss Hy,. Whenever, during the course of ex- 

 periments, the range changes appreciably a correc- 

 tion must be applied, based on the appropriate value 

 of the transmission loss H in the surrounding ocean. 

 Care should be taken to place both transducer and 

 hydrophone at such a depth that they are completely 

 hidden from each other by the wake. 



A characteristic feature of transmission measure- 

 ments of this simplest type is that, for sufficiently 

 short wavelengths, only a very narrow cone of the 

 divergent sound beam emitted from the transducer is 

 utilized, namely the solid angle subtended by the 

 face of the hydrophone at the location of the trans- 

 ducer. Thus, the instantaneously recorded transmis- 

 sion loss is for a sharply bounded layer of the wake. 

 The roll and pitch of the vessel carrying the trans- 

 ducer and hydrophone will raise and lower both 

 instruments and will cause that narrow pencil of 

 sound to traverse the wake at different depths below 

 the ocean surface. Since the acoustic thickness of the 

 wake is likely to vary somewhat vertically, corre- 

 sponding variations of the measured transmission 

 loss must be expected. 



In one respect these variations are even helpful. 

 They afford an automatic smoothing out of the verti- 

 cal variations of the acoustic thickness and thus pro- 

 duce a better representation of the average state of 

 the wake. The directivity of the sound gear is also 

 important, in so far as rolling and pitching of the 

 vessels carrying the transducer and hydrophone, to- 

 gether with possible training errors, may affect their 

 relative orientation and hence may cause fluctuations 

 in the strength of the signals received. In practice, 

 this effect cannot be separated from other fluctua- 

 tions of the signals, resulting from changes of the 

 transmission loss in the- ocean interposed between 

 transducer and hydrophone. By averaging over long 

 series of signals, these disturbing influences may be 

 minimized, though perhaps not fully eliminated. 



32.3 TRANSMISSION LOSS ACROSS 

 WAKES 



32.3.1 One- Way Horizontal Trans- 

 mission Loss 



Transmission loss in wakes has been investigated 

 comprehensively only for five vessels of the destroyer 



