Orientation dependence of the acoustic backscatter for elongated zooplankton

Abstract

The width of the main lobe of the acoustic backscatter directivity pattern of decapod shrimp (Palaemonetes vulgaris) is examined versus acoustic frequency. Using the distorted wave Born approximation (DWBA) and the geometry of a prolate spheroid, an analytic formula for the backscatter cross section as a function of orientation angle is derived. A directivity pattern is determined from the analytic formula and the width of the main lobe (beam width) is computed. The relationship between beamwidth and acoustic frequency is presented in plots of beamwidth versus ka and L/λ. The model is adapted to experimental limitations of animal motion, discrete sampling and observed side lobe levels. The backscatter directivity patterns of live decapod shrimp, determined experimentally at frequencies between 72 and 525kHz, are presented. A non-monotonic relationship between beamwidth and frequency is illustrated in this study. This relationship is in contrast to the monotonic relationship exhibited when sound scatters off of an impenetrable flat plate. Reasonable agreement is found between the theoretically predicted beamwidths and most experimental data, where the beamwidth was more-or-less oscillatory about a mean value of 19°. The structure can at least be partly explained by scattering theory.