A set of empirical equations has been developed for use in determining the target strength or acoustic cross section of an individual fish at any insonified aspect as a function of fish size and insonifying frequency in the range 1?L/λ? 100, where L is fish length and λ is acoustic wavelength. The equations were developed by interpolating experimental data obtained by insonifying individual fish as they were rotated about one of their principal axes. It was found that acoustic cross section σ is proportional to slightly less than L2 for each aspect, indicating that σ is approximately proportional to insonified area. Since σ is almost proportional to L2, a modified set of empirical equations was developed with σ exactly proportional to L2, thus eliminating the dependence of σ on frequency. The resulting errors are relatively minor and in some situations the modified equations lead to considerable simplifications which make their use quite convenient.

Experiments are described in which the dorsal-aspect target strengths of a number of individual teleostean fishes of eight species were measured at various frequencies. The results of these experiments indicate that the variations of target strength with frequency are different for fishes in two major teleostean groups, the malacopterygians and the acanthopterygians. These results are combined with results from eight other sources and an empirical equation approximating the dorsal-aspect target strength of an individual fish determined for 0.7⩽L/λ⩽90, where L is the fish length and λ is the incident acoustic wavelength. The combined results are compared to similar results for the maximum side-aspect target strength of an individual fish, and curves showing the trend of dorsal-aspect and maximum side-aspect acoustic cross sections of an individual swimbladder-bearing fish are presented for all L/λ⩽90.

A new model of a swimbladder-bearing fish has been developed in order to provide improved predictions of the resonant frequency and acoustic cross section of such a fish. The model consists of a small spherical shell in water, enclosing an air cavity which supports a surface tension. The shell is a viscous, heat-conducting Newtonian fluid, with the physical properties of fish flesh. A comparison of the results obtained with the new model to experimental data indicates that the new model constitutes a definite improvement over previous models. The new model can predict the high values of damping and elevated resonant frequencies that previous models could not. The model appears to be most accurate for fish in which tension in the swim-bladder wall has a minor effect on resonant scattering. This includes the fish which are of interest in studies of volume reverberation and therefore, the new model should be of considerable value in such studies.

A new low-frequency scattering model for small to moderately sized fish schools has been developed. The model, which uses a mathematical formalism based upon the harmonic solution of sets of coupled differential equations, allows a verified swimbladder scattering ‘‘kernel’’ for the individual fish to be incorporated. It includes all orders of multiple scattering interactions between fish, and calculates the aggregate scattering field by coherent summation. Application to simulated ensembles of closely spaced fish indicates significant deviations from incoherent scattering returns. Peak target strength reductions, and shifts in the resonance frequency, appear due to multiple scattering. The target strength also varies strongly with frequency as a result of interference effects. When applied to widely dispersed ensembles, the model reproduces the results of incoherent scattering. For larger ensembles, at greater depth, the model predicts sharply reduced target strength values around the main resonance. The ensemble effects of a school on the scattering of any single individual show more fluctuations as the school size increases. By reducing the viscous damping in the scattering kernel, the model can also describe scattering from small bubble clouds. The model has been applied successfully to fit experimental broadband low-frequency scattering data from schooling fish.

Experiments are described in which the target strengths of a number of individual fish were measured at various frequencies. The results of these experiments are combined with results from six other sources and an empirical equation approximating the maximum side-aspect target strength of an individual fish determined for 1 ⩽ L/λ ⩽ 100, where L is the fish length and λ is the acoustic wavelength. This result is combined with a theoretical estimate of the resonance of a fish containing a swimbladder, to produce a curve approximating the maximum side-aspect target strength of an individual bladder fish for L/λ⩽100.