Attenuation By An Absorptive Patch In A Duct

A short patch of absorptive material in a duct may provide greater attenuation per unit length of treatment than a long continuous lining of the same material. The increase in attenuation arises from wave scattering at the ends of the patch and consequent diffraction of additional energy into the absorptive material. A theoretical analysis based on a variational principle has been carried out for certain configurations that have also been studied experimentally. The theoretical results agree in the limiting cases with lumped constant analysis for a very short patch and with continuous duct analysis for a long treatment. Measurements were made in a rectangular duct of cross section 5×8 inches, terminated by an absorbing wedge and driven by a plane wave source. Absorptive patches extending the full width of one wall, and flush with the plane of that wall, were inserted in lengths of 1 foot to 4 feet. Two types of material were used: a homogeneous porous layer 2 inches thick, and a resonant structure consisting of a perforated facing, a resistive cloth, and a backing air cavity subdivided into small cells to insure a normal impedance independent of angle of incidence. Measurements were made from 100 to 1000 cps. Continuous plots of sound pressure along the duct were obtained from which could be determined the attenuation along the patch and the constants of the standing waves caused by scattered components. The measured attentuations range from 8 to 45 decibels depending on patch length and frequency. The results are in close agreement (within 3 percent in db) with theory, for strip lengths greater than three times the width of the duct. A more detailed theory applicable at shorter lengths is discussed.