THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

154 8. Acoustic Analogs, Ducts, and FiltersFigure 8.2. Fundamental mechanical, acoustical, and electrical analogs.stiffness. A number of difference situations can contribute to resistance; we canrepresent acoustical resistance in the conventional manner by a narrow slit insidea pipe segment.8.3 Distributed Acoustic ImpedanceWhat if one or more of the principal dimensions of an acoustic system is of thesame order of magnitude as a wavelength? In this case it may not be possible totreat the system as one possessing lumped parameters. The alternative is to analyzeit as having distributed physical constants. Consider a very simple case of planewaves propagating through a pipe in the positive x-direction. The characteristicimpedance of the pipe is given by the ratio of acoustic pressure to particle speed;and the acoustic impedance at any cross section A of the pipe isZ = p U = 1 pA u = ρ 0c(8.8)AThe case of such propagation in a pipe is electrically equivalent to high-frequencycurrents traveling along a transmission line that has an inductance per unit length L sand a capacitance per unit length C s . The corresponding input electrical impedanceis √ L s /C s . In compliance with the electrical analogy, we may consider the fluidin the pipe to have a distributed inertance M s per unit length and a distributed