This paper considers theoretically the propagation of compressional waves in a structure consisting of an infinite series of alternating layers of two different media which may be either fluid or solid. It is shown that such a structure acts as a low‐pass acoustic filter. A number of special cases are computed and it is found that the cut‐off frequency depends essentially on the section length and the relative acoustic impedance of the media. The problem is shown to be mathematically quite analogous to that of the propagation of acoustic waves in air through an infinite tube containing alternate constrictions and expansions. Moreover the loaded solid filter considered in a previous paper by Lindsay and White proves to be a limiting case of the non‐homogeneous medium filter of the present article.