[boyle] cavitation 159 



static pressure in a given medium the maximum amplitude depends 

 only on, and is inversely proportional to, the frequency. 



Denote the energy propagated per second per square centimetre 

 of wave front by W, 



P~ 

 Then W= 3^p(27r/) Vc = 3^ - 



pc 



If p cannot exceed po, the maximum energy transmissible per 



1 Po" 



square centimetre, per second is W^^ ~ 



2i pc 



Hence the maximum energy per square centimetre per second 

 would depend only on the static pressure in the medium and would 

 be independent of the frequency. 



In the case of the transmission of plane waves of sound in air 

 at standard atmospheric pressure and fifteen degrees centigrade, 

 p =. 00123 gms. per c.c; c = 3. 4X10" cms. per second; /?o = l-OXlO« 

 dynes per sq. cm. Therefore the maximum energy transmissible 

 would be 1.2X10^° ergs per sq. cm. per sec, or 1.2 k.w. per sq. cm. 



For various frequencies the maximum amplitude would be: 

 Frequency Amplitude 



These figures show that there is no possibility of cavitation being 

 encountered in the transmission of sound waves in air. Long before 

 the transmitted energy with vibration amplitudes of values like the 

 above are possible, the waves would be interrupted and broken up 

 by other causes. It has been pointed out by Stokes that in the 

 theory of the propagation of waves of large amplitudes we must take 

 into account that the condensations in the waves cannot, as in ordinary 

 sound theory, be treated as infinitely small; and it is clear that a 

 progressive wave of finite, very large, amplitude cannot be propagated 

 without change of type ^ Discontinuities must occur on account of 

 the more condensed portion of the wave gaining continually on the 



^Stokes, Mathematical and Physical Papers, Vol. II, pp. 51-56. 



