210 



TRANSMISSION OF EXPLOSIVE SOUND IN THE SEA 



30 



20 



J 10 



UJ 



2 



u 



llj 



o 50 

 z 

 ~ 40 



ho 



< 



i 20 



llJ 



t 10 



< 







500 



1000 



1500 2000 



RANGE IN YARDS 



2500 



3000 



Figure 15. Shadow zone attenuation of various fre- 

 quencies, as obtained by Fourier analysis of explosive 

 pulses. Ordinate of each plot is f/(/) + 20 log r + 

 a(/)r/l,000 referred to an arbitrary level, where U(f) is 

 the spectrum level, r is the range in yards, and a (/) 

 is the assumed absorption at the frequency /, as given 

 in Section 5.22. Hydrophone depth, 54 ft; cap depth 

 100 ft; sound conditions as shown in Figure 6. 



ferent frequencies suffers as the range is increased. 

 The decrease of spectrum level with increasing range 

 is due to geometrical divergence, wrhich can be ap- 

 proximately but not accurately described by the 

 inverse square law, to absorption and scattering, 

 which are known to increase with frequency, and to 

 the effect of the shadow boundary. To show the latter 

 effect more clearly it is convenient to plot the 

 quantity 



a(f)r 

 f/(/) + 201ogr+^ 



against the range r, using values of the attenuation 

 constant a{f) appropriate to sinusoidal sound of 

 frequency /. This is done for several frequencies in 

 Figure 15 for the shots at 100-ft depth of the same 

 series as has already been discussed in connection 

 with Figures 5, f>, 7, 8, 9, and 14. The plots shown 

 have been obtained by applying a correction to the 

 points given in reference 9 to bring the assumed at- 



tenuation o(/) into line with the more up-to-date 

 values given in Section 5.2.2. 



Within the direct zone, the points for all frequencies 

 lie roughly along horizontal lines, indicating that 

 divergence and normal attenuation suffice at least 

 approximately to explain the changes in size and 

 shape which the pulse undergoes. Because of the 

 deviations from the inverse square law discussed in 

 Section 9.2.3 and shown in Figure 5, of course it is 

 not to be expected that the points in the direct zone 

 will follow a horizontal line very precisely. At the 

 shadow boundary the spectrum levels start to de- 

 crease sharply; it is worth noting that the onset of 

 the sharp decrease occurs at 1,400 to 1,600 yd for all 

 cases and that, as one would expect, this range agrees 

 much better with the value of distance to the shadow 

 boundary derived from the time of rise and peak 

 pressure in Table 2 than with the value computed 

 from the bathythermograph data. Table 4 gives the 



Table 4. Shadow zone attenuation at various fre- 

 quencies on April 3, 1942. 



Frequency in kc Attenuation in db per kiloyard 



1 



3 



20 



40 



21 ± 2 



8 ± 1 



29+2 



27 + 2 



magnitude of the additional attenuation beyond the 

 shadow boundary, as obtained from the slopes of the 

 lines in the figure; the probable errors quoted are 

 based merely on the internal consistency of the data 

 shown in Figure 15, and may not represent the overall 

 accuracy of the calculation. The minimum of at- 

 tenuation at 3 kc is striking, and corresponds of 

 course to the maximum shown by the curves of 

 Figure 14. As can be seen from Table 3 observations 

 on other days, if treated in the same way, would have 

 given quite a different dependence of attenuation on 

 frequency. It is not known to what extent these dif- 

 ferences can be correlated with thermal conditions, 

 range, and the depths of source and receiver. 



In making a comparison between the attenuation 

 suffered by sinusoidal sound and the attenuation of 

 the various frequencies making up an explosive pulse, 

 we must keep in mind the limitations imposed by the 

 short duration of the explosive pulse, or rather by 

 the short period of time which is covered by the 

 record of it. For example, the measured values of at- 

 tenuation for a long pulse of sinusoidal sound can be 



