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

166 8. Acoustic Analogs, Ducts, and FiltersSOURCELOADZ SP S P L -Z LV S Z SP L -Z L(a)(b)Figure 8.11. Electrical analog of a ducted-source-load system: (a) pressure source; and(b) volume velocity source.The source-load interactions generally determine the acoustic performance of thesystem. This section provides a brief overview of characterization of acousticperformance of ducted sources. Acoustic performance of a system incorporatinga muffler as a path element is usually described in terms of insertion loss andradiated sound pressure.Figure 8.11 illustrates a basic duct system. Let P S and V S denote the sourcepressure and volume velocity, respectively. P L and V L represent the pressureandvolume-velocity response of the source-load system, respectively. Z S and Z Lare the complex source and load impedances, respectively. The equations for thecourse-load system in terms of pressure and velocity complex source representationsare given byP L =P SZ LZ S + Z LandV L =V SZ SZ S + Z LThe source at one end of a duct system constitutes a boundary condition. Thesource is generally more difficult to characterize than the termination because ofthe dynamic nature of the source (Prasad, 1991).Prior to the development of direct and indirect methods for measuring sourceimpedance, characteristic or infinite impedances were assumed for the source,but these assumptions do not normally yield valid values of impedances. Bothdirect and indirect methods for the measurement of source impedance are basedon frequency-domain analysis. Analytical modeling efforts have been carried our