APPENDIX B 
VECTOR FORM OF EQUATIONS FOR MEAN-SQUARE 
SOUND PRESSURE AND INTENSITY 
By defining the fluctuating force vector F by the relation FF, = F . F, Equations [19] 
and [25] may be written in the vector form 
1 LO Wor) O Ute (Gt wee wan 
lls aa nce te dy dy’ (79) 
16 7202 a ot r Ot r 72 r r 
Pa 
and 
1 Loe op\ i @ iPr 
16 7p,c° BQ NOG a Ot r 
By using Equation [38] and the relation u,u,; = @ - u, Equations [21], [20], and [26] may be 
written inthe form 
o 0 [a-F\2 || 9 (aF\? dfa-7FI| a APSO eae 
+— <3 |—|——_ — = 4 | —||——— — (%’-u’)| + |— @- DW] | — @’-w’) 
72 ot\ r ot fa Ot\ r ot ot ot 
4 U-F\2 Up 2 UP 2 —_— 
meee (=) - "| -«(2) Gi’) + @- w wa dy dy’ [81] 
4 ? r r 
AW r 
|2/ 2 wa 3| dy dy’ [82] 
OB \ Ot P 
