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In this paper, understanding and interpretations for mutual coupling within sonar arrays are given. Mathematically, our past mutual-coupling understanding of electromagnetic waves is successfully extended to treat acoustic sonar arrays. Physically, new acoustic-wave interpretations are given in this study. Numerical examples converge very fast and show that our mutual-coupling understanding for sonar arrays is very accurate. Our analyses are not only numerically efficient, but also give physical insights into the detailed coupling mechanisms between elements within a sonar array.