Clark and Yarnall 



of the medium is determined from a frequency domain measurement center- 

 ed at the signal frequency, -^ i.e. , from the side band structure of 

 the received signals (Fig, 5a) . The experimental configuration used 

 in the Straits of Florida studies (Fig. 3) offers an alternative ap- 

 proach. The time functions of the received signal amplitude and 

 phase (Figs. 5b and 5c) are made available by the phase coherent 

 demodulator. Since the medium itself is the phase modulator, a con- 

 version of the phase time function, 0(t) , to the frequency domain 

 obviously provides a direct measure of the medium fluctuation fre- 

 quency. In the more general case in which the index of refraction 

 remains a slowly varying function, not necessarily sinusoidal, the 

 spectrum of 0(t) determines the frequency content of the medium fluc- 

 tuation. The phase is a linear function of the change in the medium 

 and, in fact, provides a direct quantitative measure of this change 

 if the proportionality constant is known. If physical phenomena are 

 present which lead also to amplitude modulation, the spectrum of R(t) 

 is the applicable measure of the spectrum of the time varying, atten- 

 uation processes in the medium. 



In this example we have been careful to specify that inter- 

 ference phenomena are not present. The intuitive concept of a "beam" 

 of energy has been used to denote single path propagation. Unfortun- 

 ately, as we have indicated, there is little to justify the applica- 

 tion of this convenient concept to the Straits of Florida propagation 

 studies. The ray path calculations to be discussed in the next sec- 

 tion predict that the time dispersion in ray arrival times at the 

 H43 hydrophone is very long compared with the period of the 420 Hz 

 signal. Experimental results confirm this to be the case.l All 

 studies to date leave little doubt that the H43 cw signal is the 

 resultant of many interfering propagation paths, and we may assume 

 that each arrival is modulated by the medium. This might lead one to 

 the intuitive conclusion that the results of the cw experiments would, 

 at all times, be a quite erratic display of R(t) and 0(t), having 

 little in common with the simple example of coherent forward scatter- 

 ing discussed in this section. Certain of the data to be discussed 

 indicate this to be another case in which intuition fails. 



THE ACOUSTIC PROPAGATION MODEL 



An attempt has been made to construct a more realistic model 

 of propagation in the Straits. This has developed into a somewhat 

 involved exercise in ray theory and in the use of the digital com- 

 puter as a research tool. The result is, of course, still highly 

 idealized. From the theoretical standpoint, the model study has pro- 

 ven to be instructive in regard to the contribution of multipath ef- 

 fects and in regard to the physical meaning of the measure of the 

 environment provided by the Straits of Florida acoustic data. The 

 deficiencies of the ray theoretical approach at long ranges and low 

 frequency cw signals are acknowledged, ^ but in the present applica- 

 tion no precise comparisons of theoretical and experimental sound 

 pressure are being attempted, and it will be seen that useful 



312 



