1. Outdoor propagation – cylindrical field

2. Line Sources Many noise sources found outdoors can be considered line sources: roads, railways, airtracks, etc. Geometry for propagation from a line source to a receiver - in this case the total power is dispersed over a cylindrical surface: In which Lw is the sound power level per meter of line source

3. Coherent cylindrical field The power is dispersed over an infinitely long, pulsating cylinder: r L In which Lw is the sound power level per meter of line source

4. discrete (and incoherent) linear sourcesdiscrete (and incoherent) linear sources Another common case is when a number of point sources are located along a line, each emitting sound mutually incoherent with the others: Geometry of propagation for a discrete line source and a receiver - We could compute the SPL at the receiver as the energetic (incoherent) summation of many spherical wavefronts. But at the end the result shows that SPL decays with the same cylindrical law as with a coherent source: Lw The SPL reduces by 3 dB for each doubling of distance d. Note that the incoherent SPL is 2 dB louder than the coherent one!

5. Example of a discrete line source: cars on the road Distance a between two vehicles is proportional to their speed: In which V is speed in km/h and N is the number of vehicles passing in 1 h The sound power level L Wp of a single vehicle is: - Constant up to 50 km/h - Increases linearly between 50 km/h and 100 km/h (3dB/doubling) - Above 100 km/h increases with the square of V (6dB/doubling)

6. Example of a discrete line source: cars on the road Hence there is an optimal speed, which causes the minimum value of SPL, which lies around 70 km/h Modern vehicles have this optimal speed at even larger speeds, for example it is 85 km/h for the Toyota Prius

7. Outdoors propagation – excess attenuation

8. Free field: excess attenuation Other factors causing additional attenuation during outdoors progation are: air absorption absorption due to presence of vegetation, foliage, etc. metereological conditions (temperature gradients, wind speed gradients, rain, snow, fog, etc.) obstacles (hills, buildings, noise barriers, etc.) All these effects are combined into an additional term L, in dB, which is appended to the free field formula: L I = L p = L W - 20 log r - 11 + 10 log Q - L (dB) Most of these effects are relevant only at large distance form the source. The exception is shielding (screen effect), which instead is maximum when the receiver is very close to the screen

9. Excess attenuation: temperature gradient Figure 1: normal situation, causing shadowing Shadow zone

10. Excess attenuation: wind speed gradient Vectorial composition of wind speed and sound speed Effect: curvature of sound rays

11. Excess attenuation: air absorption Air absorption coefficients in dB/km (from ISO 9613-1 standard) for different combinations of frequency, temperature and humidity: Frequency (octave bands) T (°C)RH (%)631252505001000200040008000 10700,120,411,041,933,669,6632,8117,0 15200,270,651,222,708,1728,288,8202,0 15500,140,481,222,244,1610,836,2129,0 15800,090,341,072,404,158,3123,782,8 20700,090,341,132,804,989,0222,976,6 30700,070,260,963,147,4112,723,159,3

12. Excess attenuation – barriers

13. Noise screens (1) A noise screen causes an insertion loss L: L = (L 0 ) - (L b ) (dB) where L b and L 0 are the values of the SPL with and without the screen. In the most general case, there arey many paths for the sound to reach the receiver when the barrier is installed: - diffraction at upper (B) and side (C,D) edges of the screen - passing through the screen (SA), - reflection over other surfaces present in proximity (building, etc. - SEA).

14. Noise screens (2): the MAEKAWA formulas If we only consider the enrgy diffracted by the upper edge of an infinitely long barrier we can estimate the insertion loss as: L = 10 log (3+20 N) for N>0 (point source) L = 10 log (2+5.5 N) for N>0 (linear source) where N is Fresnel number defined by: in which is the wavelength and is the path difference among the diffracted and the direct sound.

15. Maekawa chart

16. Noise screens (3): finite length If the barrier is not infinite, we need also to consider its lateral edges, each with its Fresnel number (N 1, N 2 ), and we have: L = L d - 10 log (1 + N/N 1 + N/N 2 ) (dB) Valid for values of N, N 1, N 2 > 1. The lateral diffraction is only sensible when the side edge is closer to the source-receiver path than 5 times the effective height. S R h eff

17. Noise screens (4) Analysis: The insertion loss value depends strongly on frequency: low frequency small sound attenuation. The spectrum of the sound source must be known for assessing the insertion loss value at each frequency, and then recombining the values at all the frequencies for recomputing the A-weighted SPL. SPL (dB) f (Hz) No barrier – L 0 = 78 dB(A) Barrier – L b = 57 dB(A)