He eye Bes cele T., 7,’ dy dy’ a 
1617p, {j OMe ia oe if 
and 
eal SDN or coin San ie T,’ dy dy’ 
16 7p,c [ p22 rd - 
In order to facilitate their use in actual cases, Equations [19], [21], [25], and [26] have been 
expanded and are given in Appendix A. Some physical insight is obtained if.the equations 
are examined in their vector form. For this reason, the equations for the mean-square sound 
pressure and the intensity are given in vector form in Appendix B. 
SPECIAL CASES 
The general sound field is too complicated to visualize readily, so in order to gain 
insight intothe general sound field a few special cases will nowbe examined. Four cases 
will be examined in some detail: (1) single dipole; (2) single lateral quadrupole; (3) single 
longitudinal quadrupole; and (4) quadrupole radiation from isotropic turbulence. Here the 
word ‘‘single’’ signifies a distributed multipole of one type and one orientation rather than a 
point multipole. A discussion of the changes in the spectra as determined by pressure meas- 
urements at various distances from these sources will be found on page 17 of this report. 
The sound field of a single dipole oriented along the z-axis will be discussed first. 
Substituting 7 = 7 = 3 into Equations [19] and [25] gives 
p? —afs — cos 20(Ris SRR) over [27] 
162 
and 
1 Le a congemag th, a? 
ee | — cos?6 FF,’ dy dy [28] 
16 7° poe 
The intensity is purely radial and has no induction near-field component. 
