For a narrow band of frequencies around the angular frequency » in the spectrum of F, 
or in the sound radiated by the dipole, Equation [27] may be written in the form 
aD 1 1 iekroorarr ce? 
D -— | — cos Ou Er 1+ dy dy’ = (29) 
16 72c? r2 202 
Tr @ 
This indicates that there is an induction near-field term which changes the usual 1/r? varia- 
tion of the mean-square sound pressure when the square of the quantity, wavelength divided 
by 277, is significant in comparison with one. The sound intensity shows no change 
in variation with r upon entering the induction near field. In any plane containing the axis 
of the dipole, the intensity pattern is the familiar ‘‘figure eight”’ of cos? 6. 
The sound field of a lateral quadrupole oriented along the z,- and z,-axes will now be 
examined. Equation [21] gives the mean-square sound pressure for this case to be 
Fee \ 4 sin? cos? de0s? ( Fi Boy g fF Ts 
eae is N3isali3' 2B ibe} 34S} 
pic i ale 
+9 2 iF 7 dy dy’ [30] 
Similarly, from Equation [26], the sound intensity for this case is 
4 dei Een eee 
= rare sin? @cos’ cos? d T3713 ty ty [31] 
167° poe r 
The intensity is purely radial and has no induction near-field components. 
For a narrow band of frequencies around the angular frequency in the spectrum of 
T, or the sound radiated by the lateral quadrupole, Equation [30] may be written as 
2 4 
+9 
Tr @ rT @ 
== 4 tL ocr 
2 DP 2 2 
= any as i 0 0 1 
Dp \f 2 13213 Sin® 9cos* Ocos” } ( +3 
dy dy’ (32) 
16774 
The polar patterns of all terms in the mean-square sound pressure and the intensity 
are the same for the lateral quadrupole. In the z, z,-plane the pattern has the “‘clover leaf”’ 
shape shown in Figure 2. On the surface of any cone of constant 0 the pattern is a ‘‘figure- 
eight’? shape. The three-dimensional pattern may be described as four *‘beaver tails.”’ 
The sound field of a longitudinal quadrupole oriented along the z,-axis will be exam- 
ined next. The mean-square sound pressure, by substituting ¢ = 7 = 1 = m = 3 in Equation [21], 
is 
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