The sound field in the Fresnel zone of an axially symmetric plane emitter with nonuniform vibrational velocity distribution

On the basis of the Rayleigh integral, the formula is obtained for the sound pressure created by an axially symmetric plane emitter in a rigid screen with nonuniform distribution of the normal vibrational velocity component and with a harmonic vibration mode. The formula was obtained under a condition weaker than that of finding the observation point in the Fraunhofer zone. The condition requires smallness not of the emitter dimensions in comparison to those of the Fresnel zone covered from the observation point, but only values less than the square root from the ratio of the distance of the observation point to the center of the emitter to one-half of its radius. In the case of a vibrational velocity distribution in the form of a polynomial of even powers of the radial coordinate, the field at the symmetry axis is represented as a finite sum of elementary functions.