The probability density function (PDF) of the peaks of the envelopes of sonar echo from live fish were measured at beam aspect. The measurements were made at 220 kHz and in a waveguide. The fish was the common shiner (Notropis cornutus) and was about 120 mm (about 18 acoustic wavelengths) long. The PDF of the echoes was approximately Rayleigh when the fish was moving gently. The backscattering cross section equaled 4.2×10−5 m2. Transformation of the PDF’s to a target strength display in decibels displaced the maximum of the PDF to the target strength equaling 10 log10 (σbs/A0)+3 dB where σbs is the mean backscattering cross section and A0=1 m2. The target strengths of the common shiner (120 mm) and the mummechog (Fundulus heteroclitus, 100 mm) were measured as a function of aspect angle. Comparison of the experimental measurements and Love’s empirical target strengths for any aspect showed that the measured target strengths at broadside aspect were about the same and the target strengths at other aspect angles were several decibels less than Love’s values. Linear arrays of point scatterers were chosen to match the gross aspect dependence of the target strengths of the fish. The lengths of the arrays were 6.5 mm for the common shiner and 16.5 mm for the mummechog. These lengths were less than the lengths of the corresponding fish’s swim bladders.
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Huang et al. (1980) studied this question.