Efficiency of Circular Sources and Circular Arrays of Point Sources with Linear Phase Variation

The intensity and power radiated from circular ring sources and circular arrays of point sources are derived from first principles. The shape of the radiation patterns and efficiency of power output are studied as a function of phase changes between different parts of the source and of the ratio of the over‐all source dimensions to the wavelength of the sound field. These expressions are applicable to the reduction of noise from such sources as centrifugal and axial blowers and aircraft propellers. The relationship between the mathematical phase parameter and such mechanical quantities as the number of blades is described. As in the case of the linear source the radiated power drops if the phase parameter exceeds a certain critical value. However, the drop in the power for the circular source is greater than that for the line source. For the circular source alone the anomaly exists wherein the power—at most ratios of the source diameter to sound wave‐length greater than about 0.6—is greater for a source “...