indicating that the spectral density at high frequencies varies as the reciprocal of the 

 two-fifths power of the frequency cannot, of course, correctly describe the spectra 

 of real cavitation noise, if only because of the physical requirement of finite energy. 

 The departure is simply a manifestation of the fact that the high-frequency portion 

 of the spectrum is determined by details of the "spike" of sound pressure which are 

 not given correctly by the incompressive and acoustic theories. 



The spectrum of the sound: experimental. — Figures 7 and 8 show examples 

 of spectra of cavitation noise obtained experimentally by Mellen [20] and Jorgensen 

 [21] respectively. Three features characterize the spectrum: the location of the peak, 

 and the two exponents corresponding to the asymptotic behavior at low and at high 

 frequency. At high frequencies, the spectral density is observed to vary roughly as 

 the reciprocal of the square of the frequency ( — 6db/octave). This feature of the 

 spectrum suggests that the sound pressure undergoes a sharp rise of the nature of a 

 shock. Direct evidence of the sudden rise, such as an oscillograph record showing 

 it, is difficult to obtain because of the extremely short time interval which must be 

 resolved (perhaps l(h 7 second or smaller). However, such records showing indications 

 of a shock have been obtained through the use of tiny barium titanate transducers 

 [22]. Shock waves emitted by collapsing cavities have also been shown by Schlieren 

 photography [23, 24]. 



Compressive flow in the collapse of a cavity. — The explanation of the outgoing 



Po 



.000 



.001- 



Figure 8. The measured spectrum of noise produced by a cavitating jet. The symbol p represents 

 the rms pressure in a half-octave band of frequency, at a point four diameters off the axis and 

 four diameters downstream from the orifice. The different spots represent different combinations 

 of jet diameter, D (%, %, and 1 Vi inch), and ambient pressure, P ( Vi , 1# and 2 atmos). U, is 

 the efflux velocity; a is the cavitation index, 2P„/pU 2 . (From Jorgensen [21]) 



253 



