208 Lecture 12 
107-2 
M Harrison 
\ (Flow Noise) \ 
\ 
10-3 T ay 
Water Tunnel ORL 
1075 
ENERGY SPECTRUM FUNCTION, F(n), sec 
Fig. 12.10. Power spectrum of 
boundary layer turbulence. 
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io 8 
10 10° 10° 10 10 
FREQUENCY, n, cps 
to the temperature recordings are obtained when white noise is passed through 
a high-pass or low-pass filter and the filtered output is observed with an oscil- 
loscope. The cutoff frequency can always be identified by the predominant peri- 
odicity of the output, which has a period equal to the cutoff period of the filter. 
Changing the cutoff frequency of the filter changes the periodicity of the output. 
Another very similar phenomenon is observed in the detection of sound by 
an early type of condenser microphone. The transients of the sound generate 
decaying vibrations of a period equal to that of the cutoff period of the micro- 
phone. The ear, which integrates over only a short interval of time, perceives 
these transients as a hiss at the frequency of the microphone. 
In a long-time Fourier analysis, the fluctuations cancel, but they always 
appear in a short-time analysis of the noise, such as that performed by the 
human ear. This fact is illustrated by Fig. 12.11 in which the left half of the 
curve is in antiphase to the right half of the curve. The contributions of the two 
halves of the curve cancel in the Fourier integral. If, however, the Fourier in- 
tegration is limited to the right or left half of the curve, Fourier analysis leads 
to a predominant component of a period approximately equal to the period of the 
fluctuation of the curve. 
The generation of the cutoff in the power spectrum at a wavelength equal 
to about four times the depth of the measurement still needs explanation. Un- 
