Acoustical modeling for use in the engineering design of waveguides

Many situations exist in which sound waves are constrained to propagate in waveguides. If the diameter is small compared to the wavelength of sound to be propagated, it implies that only plane waves propagate in a cylindrical tube or spherical waves in a horn. The input impedance of any axially symmetric waveguide is of primary importance to simulate fluid resonance behavior before an actual engineering design is made. This acoustical model implements a frequency domain characteristic based on the ABCD transformation matrix [A. H. Benade, J. Acoust. Soc. Am. 83, 1764–1769 (1988)]. The input impedance is expressed in terms of the ABCD matrix, which relates ‘‘input-end’’ (p1, u1) pressure and flow to the ‘‘output-end’’ pressure and flow (p2, u2). Any complicated waveguide system can be treated as a combination of a number of uniformly shaped waveguides, and thus the resultant ABCD matrix can be the product of the individual matrices from the input to the output ends. Experimental results as well as numerical predictions for a nozzle used in an industrial ink jet printer are presented and discussed.