412 BELL SYSTEM TECHNICAL JOURNAL 



electrical network theory to the design of electro-mechanical systems men- 

 tioned in the introduction. 



Aside from this electro-mechanical field special applications have been 

 made in acoustic and mechanical apparatus where problems occur similar 

 to those solved by electrical means. In all of these applications it is the 

 filter type structure that is applied. 



One of the first of these applications was the acoustic filter. In ventilating 

 ducts, automobile, and other types of engines, and for many other uses, it 

 is desirable to pass a steady or slowly varying stream of air, and attenuate 

 the more rapid vibrations which constitute the undesired noise. Further- 

 more, it is desirable to pass the low-frequency variations with little or no 

 loss, since such loss increases the back pressure on the engine or blower and 

 greatly decreases their efficiency. For this purpose the low-pass filter type 

 structure is well suited since it passes a low-frequency band with little or no 

 attenuation and strongly suppresses higher frequency components. 



The rudimentary idea of the acoustic filter probably dates back to 

 Herschel (1833) who suggested the use of combinations of tubes capable of 

 suppressing certain frequencies. Following the development of electrical 

 wave filters, Professor G. W. Stewart^ showed that combinations of tubes 

 and resonators could be devised which would give transmission character- 

 istics at low frequencies similar to electrical filters. This theory worked 

 well as long as the structure was small or the frequency low, but broke down 

 for large structures and high frequencies due to the essentially distributed 

 nature of the elements. A theory of acoustic filters was given b\^ the writer 

 in 1927,^° which took account of wave motion in the elements, and this 

 theory could account for the properties of the filters to much higher fre- 

 quencies. Since then, Lindsay" and his collaborators have discussed a 

 number of acoustic type filters with various types of side branches and 

 obstructions. 



Mufl^ers existed long before the theory of acoustic filters was worked out 

 but they were designed as a series of baftles, -which introduced considerable 

 back pressure on the engine. Most recently designed mutflers have a 

 straight conducting path wdth side-branches in conformance with acoustic 

 filter theory and are proportioned to attenuate most of the frequencies 

 above 100 cycles. As a result they are considerably more effective than 



" Phys. Rev. 20, 528 (1922); 23, 520 (1924); 25. 590 (1925). See also Stewart and Lindsav 

 "Acoustics," Chap. \^I. D. Van Nostrand. 



1" A Study of the Regular Combination of Acoustic Elements, with Applications to 

 Recurrent Acoustic Filters, Tapered Acoustic Filters, and Horns. B.S.T.J. Vol. VI, 

 pp. 258-294, April 1927. 



" An excellent review and resume of the literature on gaseous and solid acoustic filters 

 is given bv Lindsav, "The Filtration of Sound I." Jour. A pp. Phxs. 9, 612 (1938): "The 

 Filtration of Sound II," Jour. A pp. Phys. 10, 620 (1939). 



