ECHOES FROM WAKES 



537 



of W for any wake across which the transmission loss 

 is less than 1 (ih. In practice, if the wake strength is 

 less than about —30 db, the echo is difficult to dis- 

 tinguish from the background. Since the theoretical 

 maximum value of W is only —16 db for a wake 

 10 yd deep, there is a relatively narrow spread of 

 values over which u(Rr) can be varied to give meas- 

 urable variations in W. 



34.3.1 



Surface Vessels 



For surface ships the transmission loss across the 

 wake is usually large. Thus in theory all surface 

 wakes should exhibit a wake strength W given by 

 equation (5). All wake strengths should be nearly 

 constant and equal to — 16 db, except for small varia- 

 tions in 10 log h, presumably not exceeding 3 db at 

 most. 



An examination of the surface vessel wake 

 strengths tabulated in Table 5 of Chapter 33 shows 

 that the wake strengths are highly variable. The 

 variabiUtj- of transmission loss, which could not 

 readily be taken into account in the measurements, 

 probably accounts at least in part for this failure of 

 the wake strengths to remain at a constant level. 



Even the average observed values of W, however, 

 cannot be compared directly with the theoretical 

 predictions. In the first place, the measured wake 

 strengths all refer to peak amplitudes. Extensive 

 measurements of reverberation records ^ show that 

 the average peak ampHtude is about 7 db higher than 

 the average amplitude; these measurements refer to a 

 segment of reverberation three to six times as long as 

 the signal length. Moreover, since the rms ampHtude 

 is about 1 db above the average amplitude, it follows 

 that — 6 db should be applied as a net correction. 

 According to the observations, this correction does 

 not change rapidly in magnitude when the length of 

 the reverberation segment analyzed is changed. Since 

 echoes from wakes are structurally similar to rever- 

 beration, it is concluded that a correction of — 6 db 

 applied to the observed values of W listed in Chapter 

 33 presumably will suffice to express them on the in- 

 tensity scale envisaged in equations (3) to (8). In 

 addition, if surface-reflected sound reaching the wake 

 is of the same intensity as the direct sound, the 

 "ictual transmission anomaly is 3 db less than as- 

 sumed; another 6 db should then be subtracted from 

 the wake strengths reported in Chapter 33 to give the 

 correct values. 



If the correction for surface-reflected sound is neg- 



lected, values of the observed wake strengths on an 

 intensity scale may be found by subtracting 6 db from 

 the values of W listed in Table 7 of Chapter 33. The 

 resulting values are shown in Table 6, together with 



T.\BLE 6. Observed and predicted wake strengths. 



the wake depths h taken from Chapter 31 and the 

 theoretical limiting values of W found from equation 

 (5). The close agreement between theory and obser- 

 vation for the larger vessels suggests that no large 

 correction is required for the presence of surface-re- 

 flected sound. This same conclusion is supported by 

 agreement between direct and indirect determina- 

 tions of submarine target strength at beam aspect, 

 reported in Sections 21.5.4 and 23.8.1 of this volume. 

 There are a few cases of anomalously high wake 

 strengths, discussed in Section 33.4. These are diffi- 

 cult to explain on the basis of scattering by bubbles. 

 One possible effect worth considering, that could in 

 principle give rise to very high wake strengths, is the 

 specular reflection of sound from wakes. As pointed 

 out in Section 28.3.4, bubbles not only scatter sound, 

 but also affect the sound velocity. If the boundary of 

 the wake is sufficiently sharp, some sound will be re- 

 flected backward. Since the reflected sound rays will 

 go predominantly in the backward direction, rather 

 than out in all directions, the resulting wake echo 

 can be quite high even though the coefficient of re- 

 flection is not very great. For the bubble densities 

 found in destroyer wakes, and summarized in Table 

 2, the reflection coefficient found from equation (85) 

 of Chapter 28 is less than 0.4 X 10~' and therefore 

 quite negfigible. It is possible that higher bubble 

 densities might be present in the highly reflecting 

 wakes of the vessels discussed in Section 33.4, but 

 this seems unlikely. These high values (see Table 5 of 

 Chapter 33) were found in early measurements in 

 shallow harbor waters and have not been reproduced 

 in later, more accurate determinations on wakes of 

 the same vessels. For example, early measurements 



