The wave analyzer shown in Figure 3 serves the function of measuring the correlation 

 in a restricted frequency band. As explained later, if observations are made using a suffi- 

 ciently narrow frequency band, it is possible to use these measurements to obtain the cross 

 spectral density between the pressure fluctuations at two points. 



The convection velocity for the partially frozen pattern of the pressure fluctuations 

 was determined by examining the correlation and cross spectral density with time delays. 

 These were produced by a delay line consisting of a multistage low-pass filter. This delay 

 line gave time delays in 40-microsecond steps up to 6 milliseconds. The delay line had a 

 usable frequency range from zero to a little above 5000 cps. 



EXPERIMENTAL RESULTS 

 SPECTRAL DENSITY OF THE PRESSURE FLUCTUATIONS 



The spectral density of the pressure fluctuations P (f) is defined as^ 



P(/) = nm y |4^(/)|2 

 where 



1 

 -T 



is the Fourier transform of the pressure fluctuations over the time 2T. 



The basis for the measurement procedure used in obtaining the spectral density begins 

 with the fact that the spectral density and the autocorrelation function of p(t) are Fourier 

 transforms.^ 



It then follows that 



ff{T) =p(i;)p(< +t)= [ P if) cos CO t df 



ff(0)=p2= j P{f)df 







According to this equation one can experimentally obtain the spectral density by measuring 

 the mean square output p^ of a narrow tunable filter of band with A/ and unity gain. 



