To obtain reasonable corrections for data taken in the near-sound field of a jet, an 
assumed distribution of quadrupoles along the jet is integrated with respect to varying dis- 
tance and angle from the measuring point. This procedure automatically includes the effects 
of the geometric near field, the induction near field, and the angular dependence of the quad- 
rupoles. To a first approximation an average distance and angle may be used. For high con- 
vection Mach numbers it may be necessary to use the equations in Appendix C. 
For the typical sound spectrum of the far-field sound of an air jet, given by the solid 
curve in Figure 5, the approximate spectrum expected from data taken at a distance of 1 ft 
from the jet is indicated by the dashed curve in the figure. The frequency corresponding to 
a 1-ft wavelength in air is about 1100 cps. The eventual change in slope at the lower fre- 
quencies is 12 db/octave, but the change in slope in the transition region between the near 
field and the far field is somewhat indeterminate because of the assumptions made as to the 
average distance 7 and the types of quadrupoles. These estimates can be made sufficiently 
accurate, however, toenable one to make reasonable corrections to data taken inthe near- 
sound field. 
The case of sound from a turbulent boundary layer is also of interest. Aspects of this 
problem have beendiscussed by Lighthill,?* Powell, > Phillips, * and Curle.” Curle has 
shown, in general, how dipole radiation results when a solid body or boundary is present in 
the turbulent field. For curved boundaries dipoles with axes perpendicular to the boundary 
arise from the fluctuating pressures on the boundary, and dipoles with axes parallel to the 
boundary arise fromthe fluctuating shear forces. The dipoles from the fluctuating forces 
exerted by a plane boundary on a fluid have been shown by Phillips to have their axes parallel 
to the boundary. If these dipoles are assumed to be of approximately equal strength in the 
two coordinate directions in the surface and if, for convenience, the origin of coordinates is 
Approximate Expected 
Spectrum at | ft from Jet 
db Relative to Arbitrary Pressure Level 
62.5 125 250 500 1000 2000 4000 8000 16,000 
Frequency in cps 
Figure 5 — Typical Air Jet Noise Spectrum and Approximate Changes that Occur 
if Data Are Taken at an Average Distance of 1 Foot from the Jet 
18 
