The field of an equivalent multipole composite radiator in a waveguide

The possibility of replacing a spatially extended volume low-frequency sound source, which forms a three-dimensional directional field in the far-field zone, by an equivalent multipole source is considered. Developing the ideas of L.M. Brekhovskikh, who obtained the solution for a monopole, exact and simplified models of the source field are constructed in the form of superpositions of multipoles of various orders. The models are considered in the integral, mode, and ray approximations applied to the unbounded space and homogeneous and plane-layered waveguides. The results of computations are presented, and the conclusion is made that the contribution of the vertical dipole and quadrupole components to the interference structure of the field amplitude in a waveguide decreases with an increase in the distance from the source. The phase structure is found to be stable regardless of the type of the complex multipole source.