A middle layer (22) having partitioned cavities (28) is sandwiched between an imperforate sheet (24) and an optional perforate sheet (26) to form a low resistance acoustic liner (22). A preferred method of manufacture of the low resistance acoustic liner (20) uses aspects of the buried septum technique including placing an uncured imperforate septum (36) between a support layer (32) and a partitioned cavity middle layer (22), pressing the middle layer into the imperforate sheet (24) and through the support layer (32), curing the imperforate septum 36 to form the imperforate sheet (24), removing the support layer (32), and attaching a perforate sheet (26) of roughly at least 15% open area to the top side of the middle layer. A preferred embodiment of inner and outer linings (47), (49) is provided. Each lining includes a combination of annuluses of absorptive and/or low resistance liners (51), (53). A first arrangement of engine acoustic linings includes alternating sections of absorptive liner with low resistance acoustic liner, one after the other. The low resistance acoustic liner scatters low mode order noise into a range of noise orders, including both high and low mode order modes. The absorptive liner absorbs the high mode order noise and dissipates it as heat. A second arrangement of acoustic linings includes a splitter (70) having a portion formed of low resistance liner (72).