An approximate solution to sound radiation from slender bodies

Approximate analytical expressions are proposed to calculate the sound pressure radiated from axisymmetric slender bodies. The spatial Fourier spectrum of the velocity surface distribution may be continuous but is specified to be of limited bandwidth with the highest wave number smaller or in the order of the inverse of the body length. The source strength distribution of the integral solution is determined from an asymptotic expansion of the solution with respect to the slenderness ratio near the body surface. The radiated pressure has a wave representation and is expressed in terms of the helical wave components of the Fourier transform of the surface velocity. The formalism is valid at low and medium frequencies where the acoustic wavelength is larger or in the order of the radius of the body. It is shown that most results of previous works can be reproduced in a systematic way from the derived formulas for the radiated pressure.