Chapter 7 

 INTENSITY FLUCTUATIONS 



IT IS CLEAR from the preceding chapters that the 

 sonar officer or the research worker cannot pre- 

 dict with precision the sound field intensity in the 

 vicinity of a caUbrated sound source, no matter how 

 complete his information on oceanographic condi- 

 tions. Chapter 5, in particular, mentions the wide 

 range of sound field levels which are recorded under 

 identical or nearly identical oceanographic condi- 

 tions. 



This chapter will be concerned with the variability 

 of the sound field which is found when a succession of 

 single-frequency signals are transmitted over the 

 same path and received and recorded through the 

 same receiving sound head and stack. This variability 

 within a single sequence of sound signals has been 

 subdivided into fluctuation, changes in intensity ob- 

 served to occur during seconds or fractions of a 

 second: and variation, a slow drift of the average in- 

 tensity, which becomes noticeable in the course of 

 minutes. This division between short-term and long- 

 term variability can be justified on practical grounds. 

 Variation may well be correlated with those large- 

 scale changes in the thermal structure of the ocean 

 which would be revealed by a continuously recording 

 bathythermograph. Fluctuation is caused by mecha- 

 nisms which cannot be observed by means of any 

 oceanographic instrument in current use. This chap- 

 ter will be concerned, exclusively, with the short-term 

 variability of the sound field. The longer-term varia- 

 bility has already been discussed in Chapters 5 and 6. 



The first section of this chapter will set forth the 

 mathematical concepts commonly used in the de- 

 scription of fluctuation and will report the results of 

 fluctuation experiments. In the second section, the 

 significance of these experimental results will be as- 

 sessed, and the contribution of various mechanisms 

 to the observed fluctuation will be estimated tenta- 

 tively. 



7.1 OBSERVED FLUCTUATION 



7.1.1 Magnitude of Fluctuation 



In describing fluctuation quantitatively, we need 

 expressions which characterize both the magnitude 



of fluctuation — roughly the amount by which an 

 individual signal deviates from the mean for the run 

 — and the time rate at which the sound field in- 

 tensity changes. This subsection will be concerned 

 with the magnitude of fluctuation. 



Three different quantities are commonly used to 

 express the magnitude of a received signal : the pres- 

 sure amplitude (in dynes per square centimeter), the 

 intensity (in watts per square centimeter), and the 

 level (in decibels above some standard). When we 

 consider a sequence of A'^ signals received under ap- 

 parently identical conditions, we can characterize 

 this sequence by three sets of figures : amplitudes, in- 

 tensities, and levels of all the individual members of 

 the sample. Each of these three sets of figures de- 

 scribes the sample. Depending on our particular 

 viewpoint, we may prefer one or another. 



These three sets of figures can be converted one 

 into another by means of the two equations 



/ = 



2pc' 



I a 



L = lOlog- = 20 log-, 

 /o do 



(1) 



(2) 



in which a stands for the pressure amplitude, / for 

 the intensity, and L for the level in decibels. To each 

 of these three sets we may assign as an average 

 quantity the arithmetical mean, such as 



— (oi + a2 + 



+ aff). 



(3) 



and refer to these quantities as the mean amplitude, 

 the mean intensity, and the mean level of the sample. 

 These average quantities are no longer related by the 

 equations (1) and (2). 



Individual amplitudes will, of course, deviate from 

 the mean amplitude. But some of these deviations 

 will be positive, others negative, and it can be shown 

 very easily that their sum vanishes. To express the 

 spread of the amplitudes of the sample about the 

 mean amplitude, a common procedure is to square 

 the deviation of each individual amplitude from the 

 mean amplitude and to average these squared devia- 

 tions. The square root of the mean of the squared 



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