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

312 12. Walls, Enclosures, and BarriersIn this situation the reverberant field in the shadow zone of the barrier may beassumed to be the same with or without the barrier’s presence. This reverberantfield represents the minimum SPL in the shadow zone. The space average δ r of thetime-average reverberant energy density in the room without the barrier is givenbyδ r = 4W Rc = p2 rρ 0 c . (12.54)For the condition stated by Equation (12.53) δ r = δ r1 = δ r2 , where the numericalsubscripts denote the regions on each side of the barrier in Figure 12.15. Equation(12.54) can now be rewritten aspr2 2 = 4Wρ 0cR . (12.55)Here pr2 2 denotes the mean-square pressure in the reverberant field of the shadowzone of the barrier. Our next step is to include the mean-square pressure pb2 2 inarea 2 at the location of the receiver due to the diffracted field from the edges ofthe barrier, and this is given by (see Moreland and Musa, 1972):n∑pb2 2 = 1p2 d2= pd2 2 3 + 10N D (12.56)ii=1where pd2 2 represents the mean-square pressure attributable to the direct field withoutthe barrier, the Fresnel number N i is defined bywhereN i ≡ 2d iλ(12.57)d i = difference in direct path and diffracted path between the source and receiveλ = wavelength of the soundand D is the diffraction constant defined by 2n∑ 1D ≡. (12.58)3 + 10Ni=1iIn the case of Figure 12.16, the following path differences exist:d 1 = (r 1 + r 2 ) − (r 3 + r 4 )d 2 = (r 5 + r 6 ) − (r 3 + r 4 ) (12.59)d 3 = (r 7 + r 8 ) − (r 3 + r 4 )2 In some literature the alternative definition for the diffraction coefficient is given byn∑ 1D =3 + 20Ni=1i