THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

Example Problem 315.16 Shortcomings of the Sonar Equations 437Estimate the echo time duration of an explosive echo from a beam aspect submarinepatrolling shallow water.SolutionFrom Table 15.5 and Equation (15.24), the time duration is 0.1 + 100 + 10 =110.2 ms.15.15 Overview of the Sonar EquationsA summarization of the sonar equations may be listed as follows:Active sonars (monostatic)Noise backgroundReverberation backgroundPassive sonarsSL − 2TL + TS = NL − DI + DT. (15.25)SL − 2TL + TS = RL + DT R . (15.26)SL − TL = NL − DI + DT N . (15.27)The detection threshold (DT) differs quantitatively for reverberation and for noiseand so it carries subscripts to denote the difference.15.16 Shortcomings of the Sonar EquationsThe sonar equations expressed in terms of intensities may not always be completefor certain types of sonars. For example, the short-pulse sonars need theaddition of the echo duration to account for time stretching caused by multipathpropagation. It must also be realized that the sea is an ever-stirring medium thatcontains inhomogeneities of different sorts, with irregular boundaries with the topmostboundary on the move. Multipath propagation tends to predominate, since somany of the sonar parameters fluctuate erratically with time. Other irregularitiesmay occur because of internal changes in measurement equipment and possiblereconfiguration of the platform on which the equipment is mounted. In essence,the “solutions” proffered by the sonar equations really constitute a “best estimate”time average of what is really a stochastic problem. Thus, precise calculations to,say the nearest tenth of a decibel are exercises in futility, and the solutions mustbe considered “best guesses” or “most probable” values.