544 



SUMMARY 



PROJECTORh 



Figure 4. Range from transducer to wake. 



logarithm of the ratio of rms pressures at a point one 

 yard from the projector and at a point r yards away; 

 and ^ is a wake index based on the transducer pattern 

 which differs for different conditions. 

 Equation (6) may be written 



£ = ^ - 2ff + T„ (7) 



where Tu. is the target strength of the wake. Then 

 Tu, is related to W, the target strength of a one-yard 

 length of wake, by the equation 



7^„ = TF + 10 log r + *. (8) 



While in some ways it is convenient to picture the 

 quantity W , called wake strength, as representing the 

 target strength of a one-yard length of wake, Chapter 



Figure 5. Wake target strength as function of wake 

 strength and range. 



33 — especially Sections 33.1.1 and 33.1.3 — should 

 be studied for a full understanding of the physical 

 meaning of wake strength. In particular, it should 

 be noted that, according to equation (8), the target 

 strength of the wake r„ depends on the transducer 

 pattern and on the range over which the echoes are 



received. Values for Ty, for different values of W and r 

 may be found from Figure 5 if ^ is known. These re- 

 lationships all assume that both the top and bottom 

 of the wake are in the sound beam. 



Since the echo fluctuates, the rms pressure will not 

 be constant within one echo. In this summary, the 

 rms pressure is averaged within each echo and then 

 over several echoes. If in each echo the peak rms 

 pressure recorded is taken and then averaged over 

 several echoes, the wake strength W and the echo 

 level E will be about 6 db higher than the values 

 given here. 



35.3.1 



Long Pulses 



For pulses of duration r sufficiently long so that 

 ct/2 exceeds the extension of the wake along the pro- 

 jector axis, reasonably good predictions of the wake 

 strengths of surface vessels and submarines can be 

 made. 



If the attenuation Hw across the wake exceeds a 

 few decibels, the wake strength W is given by 



W = 10 log s + 10 log h (9) 



where h is the depth of the wake in yards, and s is a 

 function of frequency only, with the values indicated 

 in Table 2. Thus the wake strength of an opaque wake 



Table 2. Dependence of reflection coefficient s on 

 frequency. 



10 yd deep is — 16 db at 24 kc. As shown in Figure 1 

 of Chapter 34 (see curve marked OBSERVATIONS), 

 wake strengths at 60 kc are uncertain. Values at fre- 

 quencies between 10 and 30 kc are probably correct 

 to within about 3 db. A correction of 6 db must be 

 added to the wake strengths computed from equa- 

 tion (9) in order to make them apply to the peak 

 amplitude of the average echo. For a moderately 

 directional transducer, the value of ^ in the case of 

 long pings is given by 



* = 7. + 8 , (10) 



