Most of the previous theoretical work on acoustic filtration has dealt with idealized infinite structures. The present paper is a theoretical study of finite filters such as are used in practice. Considering an acoustic structure with air as the medium with main line impedance Z
and with n
branch impedances Zb
(pure reactances) equally spaced at intervals 2l
, it develops that one can express the power transmission ratio for the structure in the simple form
, (1) where
, (2) the familiar parameter of the transmission theory of filtration (reference 2). The plot of Pr
in (1) as a function of frequency shows the presence of transmission and attenuation bands which approach those of the corresponding ideal infinite case as n
becomes large compared with unity. Comparison of (1) with the actual transmission measurements of Stewart (reference 2, pp. 170, 175) shows satisfactory agreement.
The phase change which occurs between successive sections in a filter is also computed and it is shown that unlike the situation in the infinite case the phase change is a function of the section. However, at relatively high frequencies and for large n this approximates to the total phase change along the structure divided by n. Comparison with such experimental results as are at present available yields reasonably satisfactory agreement.