ECHOES FROM WAKES 



543 



5 10 15 



TIME IN MINUTES 



Figure 3. Distance astern in yards as function of wake age and speed of wake-laying vessel. 



pendicular to the wake axis, and within 10 feet of the 

 surface, the transmission loss in destroyer wakes is 

 given by the equation (see Section 32.3.1) 



H„ = \.5{vf)'- - 3.0< = a - 3.0< 



(5) 



where/ is the frequency of the sound in kc, v the ship's 

 speed in knots, and t the age of the wake in minutes. 

 When the projector is in the wake, the factor 1.5 in 

 equation (5) should be replaced by 2.4; however, the 

 value of Hw in this case may be different for different 

 projectors, since the sound output of the projector 

 may be affected by the presence of the wake. Numeri- 

 cal values of a and Hw resulting from equation (5) 

 can be read from Figures 1 and 2, respectively; 

 Figure 3 may be used to find the distances behind the 

 wake-laying destroyer corresponding to different 

 wake ages and ship speeds. 



For the wakes of large surface vessels at speeds be- 

 tween 10 and 25 knots, the value of K^ and Hw are 

 probably much the same as those given by equation 

 (5) applying to destroyers and destroyer escorts. 



These values of Ke and Hw are averages over the 

 cross section of the wake and do not take into account 

 possible large changes in these quantities with posi- 

 tion in the wake. 



For transmission along wakes, equation (3) cannot 



be used for distances large compared to the depth of 

 the wake, since scattered sound traveling other than 

 straight paths through the wake may become im- 

 portant. In particular, the transmission loss i7,„ for 

 propeller sounds observed directly behind a ship with 

 a hydrophone at a depth of 10 to 20 ft is of the order 

 of 10 to 100 db per kyd, for frequencies between 5 and 

 60 kc. This low value may also be due in part to re- 

 duction of the absorption coefficient K^ at depths 

 greater than 10 ft in the wake (see Section 32.4). 



35.3 



ECHOES FROM WAKES 



The level E of the echo received from a wake can 

 be determined from the so-called wake strength W 

 using the equation 



E = S+W -2H +lQ\ogr + <if 



(6) 



where S is the level of the rms pressure on the axis of 

 the projector, measured one yard from the projector 

 in decibels above 1 djme per sq cm; ^ is the rms pres- 

 sure level of the echo, again in decibels above 1 dyne 

 per sq cm; r is the range in yards from the projector 

 to the wake, measured along the projector axis, il- 

 lustrated in Figure A;H\s the transmission loss from 

 the projector to the wake, defined as ten times the 



