correlation measurements the usable frequency range was up to 2000 cps. The lower limit 

 on the frequency range was imposed by wind tunnel noise and not the transducer. 



In order to prove that the active area of the transducer was sufficiently small to insure 

 that the pressure was coherent over its entire face, various size orifices were used. It was 

 found that orifices up to 0.125 inch in diameter were satisfactory for obtaining the data on 

 spectral densities. Smaller orifices were used for the correlation measurements in order to 

 improve the accuracy in the measurement of the separation distance between the transducers. 



ELECTRICAL EQUIPMENT 



The spectral density of the pressure fluctuations was obtained by the use of the 

 Muirhead-Pametrada wave analyzer. A frequency band of a nominal 10 percent was used in 

 the analysis. The levels were read on the Ballantine True rms voltmeter. In the section 

 giving the results of the measurements, the details of how to obtain the spectral density from 

 the observed data are given. 



The correlation between the pressure fluctuations at two points was measured using 

 rather simple apparatus. The basis for the method used is contained in the algebraic identity 



l^a 



(e^ + e^)^ -(fij -63)' 



2^ 2\% 



{ele^ 



2^ 2vy. 



^{e'^e^) 



where the term on the left is the correlation between e^ and e^. The bars indicate time 

 averages, e, and e ^^ are here regarded as voltages that are proportioned to the fluctuating 

 pressures j) ^{t) and Pj (0? respectively, where the subscripts denote the two points at which 

 the measurements are performed. With reference to Figure 3, the addition and subtraction of 

 the voltages were accomplished by the transformer. The time averages were accomplished by 

 the Ballantime True rms voltmeter, whose time constant had been increased to two seconds. 

 This produced satisfactory smoothing of the fluctuations. Measuring the correlations is then 

 a matter of making four meter readings, [(e ^ + e ^'^\^\ \{e ^ - e^)^]'^', {e ^Y''', and e^)'^', and 

 doing the computations indicated by the above algebraic identity. 



M< 







Wave 

 Analyzer 



Figure 3 - Schematic Diagram of the Equipment Used in the 

 Measurement of the Cross Spectral Density 



R.M.S. 

 Meter 



