228 Lecture 12 
60 FREQUENCY: 25 KC 
x= DIRECT 
x o = SURFACE ° 
EACH POINT REPRESENTS 
50 PULSES 
50 
ie) SURFACE- 
Cau RE 5 ic MP RERUECTED ¢ 
° 6) ° ° PATH 8 
g ox 
30 ) 
QO © 2 
RELATIVE 
x STANDARD 
20 © DEVIATION 
x ALONG 
** DIRECT 
PATH 
ae 
RELATIVE STANDARD DEVIATION (per cent) 
100 300 500 700 900 1100 1500 
RANGE (yd) 
Fig. 12.17, Fluctuation measurements made by the Ordnance Research Laboratory at 
The Pennsylvania State University. 
1300 
where K = <a?>xo and 
<a*>ko 
2 2 
MPS ARO ee (73) 
The coefficient of variation vy, is thus proportional to the root of the range and 
independent of the frequency. The L-range dependence seems to be certain, no 
matter what power has been assumed in the power spectrum; the frequency 
dependence, however, in only approximate. A still closer approximation to the 
Kolmogorov law (assuming m= 2 in the integrand so that integration becomes 
possible and m=, in the factor in front of the integral) leads to the result that 
scattering is proportional to the cube root of the frequency which is in good 
agreement with the experimental result. 
12.5. EXPERIMENTAL RESULTS 
12.5.1. Standard Deviation of the Transmitted Signal 
The fluctuations of the transmitted signal are usually described by their 
standard deviation and by their distribution law. The standard deviation is de- 
fined as the ratio of the square root of the mean-square deviation from the 
mean value and the mean value of the pressure 
me 2,¥2 y 1 
Vasoe <@ = Po)" >“ _ <Ap*s /2 (74) 
Po Po 
The square of this quantity is called the relative coefficient of variation. 
