In applied mathematics, the Biot–Tolstoy–Medwin (BTM) diffraction model describes edge diffraction. Unlike the uniform theory of diffraction (UTD), BTM does not make the high frequency assumption (in which edge lengths and distances from source and receiver are much larger than the wavelength). BTM sees use in acoustic simulations.[1]
The impulse response according to BTM is given as follows:[2]
The general expression for sound pressure is given by the convolution integral
p(t)=
infty | |
\int | |
0 |
h(\tau)q(t-\tau)d\tau
where
q(t)
h(t)
(rS,\thetaS,zS)
z
\theta
(rR,\thetaR,zR)
\thetaW
\nu=\pi/\thetaW
c
as an integral over edge positions
z
h(\tau)=-
\nu | |
4\pi |
\sum | |
\phii=\pi\pm\thetaS\pm\thetaR |
z2 | |
\int | |
z1 |
\delta\left(\tau-
m+l | |
c |
\right)
\betai | |
ml |
dz
where the summation is over the four possible choices of the two signs,
m
l
z
\delta
\betai=
\sin(\nu\phii) | |
\cosh(\nuη)-\cos(\nu\phii) |
where
η=\cosh-1
ml+(z-zS)(z-zR) | |
rSrR |