Abstract: From the point of view of the auto-spectrum, the local characteristic and the acoustical energy of radiation on a vibrating surface are theoretically studied in this paper. The point radiation impedance is defined as the radio of sound pressure to the vibrating velocity at any point on a vibrating surface, which establishes the relation between a vibrating surface and a sound field. Applying the Cauchy integnal theorem the chromatic dispersion relation between the real component and the imaginary component of the point radiation impedance is given, and some characteristics are discussed. The discussion of two typical sound sources, pulsating and oscillating spheres, supports the arguments of this paper.