= 
194 Lecture 11 
Writing 
PealoQoaayr «(a(S 
we then have 
(a ie 2.2 ; 
T(A,p) = Cyk? { i Jo (ee i [r(1 — v')?] exe(=3 Jo tdrdw (2) 
Let 
O_-4y 
ké 
Then 
Cnt nent ~ 2g \, -9/2 
T(A,n) = an | i, Jo(ur) Jo lr -v' 7)”7] exo( 3). ru dr du 
Op hs Sf 2-9/4 -2g 
eral : 
This result may be more conveniently written as 
2s 1 7h 
T'(,p) = exp [- +)8 (4) 
py’)? 
where 
a=? =f yA Gg 
In terms of convenient units, we have finally 
T(Q,p) = 0.098 y2W 75(1 — v!2)-2 exo )a' 
a 
a’ = 6.33H~ /°b(1—v'2)% (5) 
Let & be the angle betweenthe specular direction and the direction of scatter- 
ing. Then evidently, 
1-v?=2-(W-y)?-2cosy (6) 
.3. BACK SCATTERING 
In the case of back scattering, v=y, and the angle between the vertical and 
the direction of the incident wave is ¥/2=6. Thus, for back scattering, 
1-v'?=4 sin?6 
and 
Ys 2 i melee, -¥, 
T, = 0.0061 H’° cos*@ sin” @ exp Buch 
a! = 12.66 H~”5 bsind (7) 
where we have written T=I. for this special case (reverberation). In applying 
this equation to the calculation of reverberation intensities, a number of tech- 
nical factors, including the geometry of the situation, must be considered. How- 
