Evaluation test of circular acoustic reflector based on number theory prototyped made utilizing additive manufacturing

Abstract

As an application of number theory to the field of acoustics, acoustic reflectors with phase diffraction grating based on Galois fields or primitive roots have been studied. These reflectors have a structure with equally spaced depressions of irregular depth that diffuse acoustic wave in various directions. To generate the sequence of irregular numbers needed to determine the depth of the concavity, methods such as using a primitive element of a Galois field the remainder of the power of a primitive root of a prime number have been proposed. In either method, the depth of the depressions is taken from 0 to half of the wavelength of the sound wave to be diffused, and the spacing between the protrusion or depression is designed to be quarter of the wavelength, resulting in a rectangular shaped reflector. The proposed method not only allows the design to change from rectangular to circular, but also makes it possible to construct a structure corresponding to multiple wavelengths on a single reflector. In this report, the effectiveness of the proposed reflector will be demonstrated through a model experiment of a prototyped reflector by using additive manufacturing.