Active absorption of sound by a cylindrical absorber in a cylindrical duct

We consider the problem of sound attenuation in an infinitely long cylindrical duct, with emphasis on the absorption of acoustic power by a cylindrical device centred in the duct. It is shown that for frequencies below that of the first excited eigenmode of the duct a device with two independent active surfaces can absorb all incident power. In principle this is the case regardless of the size of the absorber.