Attenuation of sound in lined circular ducts

Abstract

In the previous report, we have used approximate expressions for the wall impedance for the discussion of sound attenuation in lined circular ducts. For instance, Eq. (2.5) has been used for the wall impedance of a circular duct lined with a resonator with a resistive screen, and Eq. (2.8) for a circular duct lined with a porous material. If the ratio of the duct radius to the liner thickness (D/L) is large and the sound frequency is large, the impedance given in Eq. (2.5) or Eq. (2.8) is a good approximation for a lined circular duct. However, when either one of these conditions is not fulfilled, the radial spread of the wave in the liner imposes some effects on the sound attenuation, whereas no wave spreading takes place in the liner of a rectangular duct. In this addendum we derive expressions for the wall impedance of lined circular ducts, accounting for the cylindrical spreading of the waves within the liner. The assumption of a locally reacting surface is still made. On the basis of the impedance thus obtained, the attenuation characteristics of a circular lined duct are computed for a wide range of parameters.