The nature of sonar echoes from a hollow metallic sphere in water is investigated theoretically in relation to the thickness of the shell and the contents of the hollow region. Steady-state solutions are presented for iron and aluminum spheres filled with water and for iron spheres with a vacuum inside. Calculated results for pulsed sound suggest that part of the echo originates from a type of flexural wave moving around the shell, which changes into a surface wave as the shell thickness increases. Significant differences in echo structure occur when the interior region is changed from water to a vacuum.
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Robert Hickling (1964) studied this question.