20- 



10 

 

 -10 

 -20 

 -30 

 -40 

 -50 



"Ultrasonic Spectrum of Cavitation- 

 Noise in Water" R.H. Mellen 

 JOUR. ACOUS. SOC. 1954 



\ 



.1 



I 10 100 1000 



Frequency in KC 



Figure 7. A measured spectrum of cavitation noise. The solid curve represents the spectrum of the 

 steady noise observed at a distance of 1 meter from a metal rod, 2 inches long and 1/16 inch 

 in diameter, rotated at 4300 rpm about a transverse axis through its center. The reference level 

 for the decibel scale corresponds to sound pressure of 1 dyne/cm 2 in a 1 cy/sec band of frequency. 

 The cavities observed were about 1 mm in diameter. The pressure was approximately 1 atmos. 



quencies, the spectral density necessarily varies as the fourth power of the frequency.* 

 The oscillations in the spectrum of the sound generated by the multiple collapse do 

 not disappear from the computation at the higher frequencies. However, the oscilla- 

 tions will not appear in the spectrum of the sound generated by a succession of cavities 

 which do not all grow, collapse, and rebound in exactly the same way. Accordingly, 

 at the higher frequencies the "smoothed out" spectrum is shown. The asymptotes 



* This follows from the fact that the volume of the cavity is necessarily positive during 

 its lifetime and essentially zero before and after. The magnitude of the Fourier transform 

 of the volume (the latter considered as a function of time) is then, by well-known properties 

 of the Fourier transformation, to the first order, independent of the frequency at values of 

 the latter which are small in comparison with the reciprocal of the total lifetime of the 

 cavity. Since the sound pressure is proportional to the second time derivative of the volume 

 of the cavity (Eq. (4), Sect. 2), the exponent relating the spectral density and the frequency 

 at small values of the latter is thereby determined. The conclusion applies to the spectrum 

 of the sound generated by a single cavity or by a random succession of cavities, but must 

 be modified if referred to a sequence of cavities in which the behavior of successive cavities 

 is in any way correlated. The presence of a reflecting boundary, especially a free surface 

 will, of course, alter the frequency dependence also. 



252 



