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

8.6 Ducted Source Systems—Acoustic Modeling 167Z sABCDZ r(a)Z sZ Lp r V r(b)Figure 8.12. Duct system models: (a) source-path-termination model and (b) source-loadmodel.principally in the time domain based on the method of characteristics. A number ofstudies have been conducted on the basis of modeling of the geometry of sources(Prasad, 1991).A duct system can be modeled as a source-path-termination model with asource load, as shown in Figure 8.12. These models are interrelated when thepath-termination is treated as a load. This type of model is commonly used, say,for engine-exhaust-pipe-tailpipe-radiation system. Referring to Figure 8.13, thethree most commonly used descriptors, namely, insertion loss (IL), transmissionloss (TL), and noise reduction (NR), are given by the following three equations:∣ ∣ ∣∣∣ AZ r + B + CZ S Z r + DZ s ∣∣∣IL = 20 log 10A ′ Z r + B ′ + C ′ Z S Z r + D ′ dB (8.34)Z S∣ ( ∣∣∣ 1TL = 20 log 10 A + BS2 ρc + Cρc )∣ ∣∣∣S + D dB (8.35)NR = 20 log 10∣ ∣∣∣(A + B Z r)∣ ∣∣∣dB (8.36)Here Z S and Z r are the source and radiation impedances, respectively, and A, B,C, and D are the four-pole parameters of the muffler including its upstream anddownstream ducts. The insertion loss IL is the most useful of the three descriptorsgiven in Equations (8.34)–(8.36). As the terminology implies, IL describes thereduction in the acoustic output when a muffler is inserted into an otherwise unattenuatedsystem. Radiated sound pressure level L p is also quite useful as it givesthe system output which can be used to determine IL. The other two descriptors,namely, TL and NR, do not require knowledge of the acoustic characteristics ofthe source. By their very definition in Equations (8.35) and (8.36), respectively,both TL and NR are independent of the influence of the source-load interaction.