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68 (a) (b) (c) (d) Figure 88. (a, c) Source images and (b, d) vertical profiles of OASPL for truck 50 in one-third octave bands centered at 630 and 1000 Hz. levels of the population are significantly affected by the 3.7.3 Example Model of Truck Sources exhaust noise sources. for Simulating Noise Propagation In an interesting case of truck 36, with the source distribu- Results of the Vehicle Passbys tion identified in Figure 85, the highest OASPL was localized Figures 76, 77, and 80 through 88 show the vertical distri- below the road surface. Figure 89 shows three acoustic images butions of noise sources as determined by roadside mea- of tanker truck 36 at various frequencies, which also reveal the surements. The key figures are 76 and 80, which show the source images located below the ground plane. The below- distributions for heavy trucks. Figure 76 shows the mean grade source image could be due to a combination of the A-weighted spectral and overall levels, while Figure 80 shows direct-path tire noise and reflection of tire noise off the bot- the distribution of maximum levels. The data plotted in tom of the tank. Close inspection of the photograph of this these two figures are presented in Appendix B. truck showed a distribution of piping and other structure The levels in Figures 76 and 80 and Appendix B are not nor- below the tank between the axles, which may explain the pres- malized to absolute values. They are, rather, relative weight- ence of the additional weak source in the image at 800 Hz. ings. Application of these results to the Traffic Noise Model Note also an increased level of sound in the area of the exhaust (32) requires that the levels be normalized to a 50 ft (15 m) stack in the 500 Hz band. A slight shift of the source image passby distance. The scaling process would be as follows: from the exhaust stack forward, which can be observed in the figure, is likely a result of a gradual deceleration recorded for At each height convert the levels in Table B-1 or B-2 to energy this truck. Sum the energies at all heights, then normalize to 1

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69 6m Observer S2 Sources Location ym2 S1 ym1 Ground, Reflection Coefficient = 0.8. Image Sources Figure 90. Geometry of simulated truck noise sources. Simple sources S1 and S2 represent the tire and exhaust sources, respectively. The ground is assumed to reflect sound from both sources with a reflection coefficient of 0.8, as suggested by the measure- ments made in this project with the calibration source. Note also that this model produced simulated source images that agree well with the measured ones, as was shown previously in Section 3.5.1 (see Figures 35 through 37). The source levels of S1 and S2 for the tires and exhaust, respectively, as well as the Figure 89. Source image for truck 36 in one-third two heights ym1 and ym2 are frequency dependent. These quan- octave bands centered at (a) 500 Hz, (b) 800 Hz, tities are also different for determining the mean sound lev- and (c) 1000 Hz. els and the maximum sound levels of the truck population. Table 15 gives the values of the parameters that were used to produce the vertical source distributions shown in Figures 91 Multiply the normalized energies by the energy of a total and 92. The source levels in Table 15 are all relative to 20 Pa passby measurement [i.e., the levels in Appendix A of the at 6 m and represent equivalent free-field source levels from the Traffic Noise Model technical manual (32)] individual sources. The values shown are example values for two frequencies only. To extend these values to a broader range This process can be carried out for any number of source of frequencies, one would calculate by an inverse propagation heights, as a generalization of the upper and lower emission method the levels and vertical locations of the elemental source levels defined by Equations 7 and 8 in Appendix A of the Traf- distributions that are required to replicate the one-third octave fic Noise Model technical manual (32). band profiles. In general this calculation may require a contin- The apparent vertical distribution of truck noise sources can uum of sources. be effectively simulated by a simple system of two uncorrelated The vertical profiles of the equivalent sources obtained for sources, similar to that presented in the Traffic Noise Model Figures 91 and 92 were produced using the same codes that are technical manual (32). This system is illustrated in Figure 90. described in Sections 3.2.1 and 3.6.2 and used to process the Table 15. Model parameters for simulation of vertical truck noise source distributions. Source Source Source Source Sound Level Frequency Level S1 Elevation Level S2 Elevation Metric Band (Hz) (dBA) ym1 (m) (dBA) ym2 (m) Mean Levels 500 81 0.8 63 3.5 1000 74 0.4 65 3. 5 Maximum Levels 500 89 0.7 81 3.5 1000 84 0.4 77 3.7

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70 ___o__ Measured _____ Measured _____ Simulated _____ Simulated (a) Mean levels (b) Maximum levels Figure 91. Vertical distributions of source levels for 500 Hz as measured at 6 m (20 ft) distance for heavy trucks: (a) mean levels, (b) maximum levels. ___o__ Measured ___o__ Measured _____ Simulated _____ Simulated (a) Mean levels (b) Maximum levels Figure 92. Vertical distributions of source levels for 1000 Hz as measured at 6 m (20 ft) distance for heavy trucks: (a) mean levels, (b) maximum levels. measurement data. Note that the measured source distribu- ple as a building block. Among other requirements for the tions all match the simulated ones, although as frequency adequate precision, such a model should use ground reflection increases it is clear that additional sources would be necessary coefficients as a function of frequency, improve fidelity in the to "fill out" the profiles at intermediate elevations. These vertical distribution at higher frequencies, and account for examples show, nevertheless, that a two-source model does some beamforming factors inherent in the current data. These provide a starting point that generally characterizes the appar- beamforming factors have to do with non-unity correlation ent source profile quite well. To build a complete model of the coefficients between microphone pairs that determine the pre- truck noise sources with the requisite fidelity for a highway cise relationship between the steered array output and the noise model, however, one should use the above model exam- sound levels at the reference microphone.