Poe P 
The quantity in each case gives the mean-square sound pressure at all points in the 
4ar 
sound field of an equivalent simple source. The terms that depend on 6 and ¢ indicate the 
variations of p” from the average over all directions. The last bracket in each equation gives . 
the induction near-field correction to the radiated mean-square sound pressure. 
SLOPE OF FREQUENCY SPECTRUM 
It is apparent that the effect of the induction near-field sound pressure is to enhance 
the low-frequency components in the sound spectrum as it appears in the far field. Therefore, 
the sound pressure spectrum determined from data on the induction near field will differ from 
the spectrum determined from data on the far field. The effect of the induction near field is 
to decrease the slope of the spectrum by 6 db/octave in the case of dipoles and 12 db/octave 
in the case of quadrupoles. For a narrow band of frequencies the approximate far-field sound 
pressure level may be obtained from the induction near-field sound pressure level by sub- 
tracting the quantity 
2 
72 rt e4 
ce? ct 
10 log ( + a, +a } [53] 
in each case using a mean frequency of the band and an average distance 7. The quantities 
a, and a, are to be taken from the last bracket term in Equations [49], [50], [51], and [52] for 
the four cases discussed. The application of these equations to the study of the sound from 
turbulent jets and turbulent boundary layers will now be discussed. 
SPECIAL CASES 
The case of a turbulent jet is of special interest because of its widespread application. 
The sound produced by a jet is usually considered to consist of two parts: (1) from a cylin- 
drical region of strong shear near the exit of the jet; and (2) fromthe core of the jet and a 
larger mixing region downstream. The sound from the shear layer is predominantly from lateral 
quadrupoles with axes along the jet and perpendicular to the shear layer of the jet. Thus, if 
6 is measured from the axis of a circular jet and if the observation point is at least several 
jet diameters from the jet, the term cos“ ¢ may be replaced by its average, namely 4, in the 
equations pertaining to lateral quadrupoles. As a first approximation, it may be assumed that 
the sound from the core and the downstream part of the turbulent region of the jet is given by 
the equations for the quadrupole radiation from isotropic turbulence. 
17 
