Application of the Fresnel Method to the Calculation of the Radiated Acoustic Field of Rectangular Pistons

摘要

Radiation from a uniformly vibrating rectangular piston in an infinite rigid baffle is expressed by an approximate solution in terms of the complex Fresnel integral. Although a similar ap¬proximate method has been used by others, the solution given here allows evaluation of a larger region of the field than do pre¬vious solutions. Field values for the specific cases of a λby 2λ piston and a 2λ by4λ piston are computed and compared for three methods of solution, namely, the present method, an analogous method by Freedman, and the Huygens construction. Favorable comparison is found between the present solution and the less approximate but more complicated solution employing a finite Huygens construction. Also, the present results are in essential agreement with Freedman's near the central axis of the piston. Thus, accurate field values can be derived, using the theory which is given, by the use of the tabulated Fresnel integral or by a graphical method using the Cornu spiral. The accuracy of these derived values vary with field position, but an estimate of the accuracy may be made by comparison with the specific cases which are given.