APPENDIX A 
EXPANDED FORM OF EQUATIONS FOR MEAN-SQUARE SOUND 
PRESSURE AND INTENSITY 
Equations [19], [25], [21], and [26], respectively, may be expanded by letting ¢, j, 2, 
and m take on the integral values of 1, 2, and 3 in all combinations and summing the terms. 
These equations then become 
see Be 
p= edie (44° fy ia dy dy’ [68] 
16 77c 72 
I -—— |= = AA’ dy dy’ 
r 
16 7? Poe 
[69] 
gale 20 
ay 1 1 oe c2 TSO ee OT ae STOR c4 ==> 
p? = i= BB’ +— |3BB‘+ D(D’~4B’)| + — |9BB’+ D(D’-6B’)|¢ dy ay’ 
167c4 7? 72 74 
E [70] 
1 iL || cere e = 
i = ea 52 9 (De BE) an ch? 
16 77p,c° r? 72 
I : \ : 0” Be F’) dy dy’ [71] 
eS eto 
16 77p,c° 2 72 
and 
1 i ee > 
If eerie 2 — D(G’+H’) dy dy’ 
16 72p,c> r2 r2 
where 
A =sin@ cos¢ F, + sin@ sing F, + cos 6 F, [72] 
aD 2 5 my 0.9) 2 
B = sin“ 0 cos ¢ T,, + sin” 6 sin” ¢ T,, + cos 6T3, 
+ 2(sin? 6 sind cos d T,, + sin@ cos@cos¢ T,,+sinOcos@sin¢d T,, [73] 
25 
