ABSTRACT
Several analytical approximations for ground effect have been derived. Rasmussen [1] has obtained an approximation for frequency-dependent ground effect in the form of the direct and plane wave reflected fields plus a correction. This approximation is based on the Delany and Bazley single parameter model for ground impedance (3.2). His result for the sound level relative to free field may be expressed as follows:
EA = 10 log{1 + (|R(θ)|r1/r2)2 + 2(|R(θ)|r1/r2) cos[k(r1 − r2) + α] + A2 + 2 exp(−5 cos(θ))A cos ξ [1 + (|R(θ)|r1/r2) cos[k(r1 − r2) + α]]
(6.1)
where the complex plane wave reflection coefficient, R(θ) = RR + iRI, is calculated from
RR = (R 2 + X 2) cos(θ) − 1
(R cos(θ) + 1)2 + (X cos(θ))2 , RI = 2X cos(θ)
(R cos(θ) + 1)2 + (X cos(θ))2 ,
Z = R + iX is the normalized surface impedance, α = − tan−1(|RI/RR|), A = (1 − RR)/[1 + k2(36.4r/Rse)]2 and ξ = −4 tan−1[k(36.4r/Rse)].
