D. E. Weston 53 
| 
= ff 
FREQUENCY SHIFT W 3 (faes) 
(50 Ib) 
SPECTRUM 
LEVEL 
IN 4/3 
LEVEL SHIFT W 2 (2348) 
dB 
LOG FREQUENCY 
Fig. 3.1. Spectrum scaling. 
ing laws. It is best to start with the delta function in example 4 which is well 
known as having a flat spectrum; the other pulses are derived from the one above 
by differentiation. At least the middle five of these examples have important 
applications to explosions. Example 5 is perhaps not very obvious but is actually 
the most generally occurring case. It is possibleto show from the wave equation 
that +o 
f pdt 
bade) 
falls off with range faster than p itself, and at long ranges may be taken as zero. 
It follows that at sufficiently low frequencies the f*-spectrum slope holds, as does 
the w? scaling law. These two laws are of great generality and, besides holding 
true for the radiated longitudinal elastic waves, will apply to both shear waves 
and electromagnetic waves. The arguments are developed in more detail in [9], 
together with the differing laws for two- and one-dimensional propagation. 
TABLE 3.1. Scaling Law at a Given Frequency as 
a Function of Spectrum Slope 
Frequency dependence Weight dependence 
of spectrum level of spectrum level 
P W? 
70 wi 
—2 w23 
