GENERAL SOUND FIELDS OF DIPOLES AND QUADRUPOLES 
DEFINITION OF NEAR FIELD 
66 
As used in this report, the unqualified expression ‘‘near-sound field’’ refers either to 
the region called the ‘‘induction near field’’ at distances less than a wavelength from the 
multipole source, or to the region called the ‘‘geometric near field’’ at distances from the 
sound source that are less than the order of the geometric extent of the source. In the induc- 
tion near field the particle velocity and pressure fields are not in phase in time. These fields 
contain a relatively large amount of unradiated energy that alternates between the kinetic 
and potential forms in the immediate vicinity of the multipole source. The geometric near 
field exists because an average distance from the measuring point to the source is usually 
used in presenting data for the region close to an extended source, even though the actual 
distances to the various parts of the source should be used. 
In many practical situations the regions defined by the two types of near field overlap 
and are comparable in extent, so that the effects of being in each region separately may be 
difficult to determine. The situation is further complicated by the fact that the effects of 
being in each region may tend to compensate each other. For example, if the distance from 
the nearest part of an extended multipole source is used as the characteristic distance from 
the source, 1! the rms sound pressure in the induction near field varies inversely as the square 
or some higher power of the distance from the source, and in the geometric near field the rms 
sound pressure may be nearly independent of the distance from the source. 
SOUND FIELD OUTSIDE A FIELD OF FLUCTUATING 
FORCES AND STRESSES 
The general expressions derived by Lighthill for density fluctuations in the medium 
outside a turbulent region have been expanded and applied, up to now, only for the region many 
wavelengths from the turbulent region. The purpose of this report is to expand these general 
expressions also for the region defined by the induction near field. As has been done for the 
radiation field, a number of special cases will also be discussed because under some practical 
conditions one type of multipole may predominate sufficiently to permit an approximate descrip- 
tion of the sound field by one set of simplified equations. 
By using the relation between density fluctuations and pressure fluctuations, the instan- 
taneous sound pressure p at time ¢ and point z outside aregion of fluctuating forces and a re- 
gion of fluctuating stresses, as sketched in Figure 1, is given, respectively, by the volume 
integrals 
1 a {F; a : 
p = - — |—|— ]ady (Equation 11, Reference 1) [1] 
4a Jou,\r 
