Lecture 3 
wn 
oo 
at 100 yards) 
iz Theory 
Experimental points (octave) 
| 8 501b 
o IIb 
x 0-002 Ib 
Energy Flux Spectrum Level (dB wrt. lerg cm” cycle 
2 4 6 810 2 4 68100 2 4 6 81000 2 4 6 810000 2 
Frequency (c/s) 
Fig. 3.4. Source levels for 7-fathom charges scaled to 1 lb. 
Note that there are regions in Fig. 3.5 with dependence on f?, f° and f~?. The 
high-frequency bubble pulse gives an f~* law, and just below the spectral peak at 
the reciprocal of the bubble-pulse frequency there is a region with a law close 
to f*. The latter arises because of the particular values of the impulses / and 
intervals T; the last illustrationin Table 3.IV is closer to example 6 of Table 3.II 
than to example 5. There is a sort of cancellation which in practice is both im- 
perfect and variable, so that the experimental levels in this region are higher 
than the simple theory (see Fig. 3.4) and also rather variable. 
TABLE 3.1V. Underwater-Explosion Pulse Shapes and Spectrum Equations 
Schematic shape Spectrum equation 
Description 
2 
2p 
Shock E)(f) = a 
pel 15 +47 f ) 
8 Tsu 
Bubble Be (ee 
pe\4Ai +47 F 
Impulse E, w=) [tt + I, cos2 mT, + 1, cos27fT3 — Nsin2 7£T3\7 
Cc 
+11 sin2 7fT; + [7 sin2 7fT3 — N(1 — cos anit)” 
where N=Io +1, +12/27T; 
