The Neumann boundary value problem for the Helmholtz equation within the quarter-space has been considered in this paper. The Green function has been used to find the acoustic pressure amplitude as the approximation valid within the Fraun-hoffer's zone for some time-harmonic steady state processes. The low fluid loading has been assumed and the acoustic attenuation has been neglected. It has also been assumed that the vibration velocity of the acoustic particles is small as compared with the sound velocity in the gaseous medium.

The axisymmetric problem of acoustic impedance of a vibrating annular piston embedded into a flat rigid baffle concentrically around a semi-infinite rigid cylindrical circular baffle has been undertaken in this study. The Helmholtz equation has been solved. The Green’s function valid for the zone considered has been used for this purpose. The influence of the semi-infinite cylindrical baffle on the piston’s acoustic impedance has been investigated. The acoustic impedance has been presented in both forms: integral and asymptotic, both valid for the steady harmonic vibrations. Additionally, the acoustic impedances of the piston with and without the cylindrical baffle have been compared to one another. In the case without the cylindrical baffle some earlier results have been used