ee Beh 
9 Po | fF, dy| cos 0 
[59] 
P 8 7p ytc> 
for a dipole, 
i 2 = 
Or | fT,, ¢7| sin 0 cos 0 cos¢ 
RS NRT TSS Ee [60] 
y 8 TP ote 
for a lateral quadrupole, and 
1 2 aA 
%@ Po" ities dy| cos? 6 
a Ni 161] 
4 
P 8mpyre 
for a longitudinal quadrupole, where K = K (y,¢-7/c) is the ‘‘mass rate density’’ or acoustic 
source strength per unit volume of the sources. 
In the induction near field the ratio is equal to the ratio of the particle dis- 
1 2 
reanolg /P 
placement to twice the radial distance from the multipole, with an additional angular depend- 
ente for the higher-order multipoles. In the induction near field of the four cases above, the 
ratios are, respectively: 
1 
fs p v2 = 
9 Po lf K dy| 
= —______——_. [62] 
P 87p,o" re 
1 2 4 
Bw If F, dy] (1+ 3cos? 6) 
$$ |= —<<$<___. ———_—_ [63] 
p Brp yor |cos 6| 
1 
2 se 2 : 
9 Po” |fT,, dy| 319 sin? 6 cos? 6 cos? ¢ + cos* (cos? 6 - sin? 6) + cos*@sin? 4] 
Dp 87p,o* ° |sin 6 cos 6 cos d| 
[64] 
21 
