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THE ROYAL SOCIETY OF CANADA 



portion less dense. "The wave becomes, so to speak, continually 

 steeper in front, and slopes more gradually in the rear, until a time 

 arrives at which the gradient at some point becomes infinite. After 

 this stage the analysis ceases to have any real meaning." (Lamb).' 



Considering cavitation of sound in water, e.g., sea-water, as in 

 the case of under-water signalling: 



p = 1 . 02, and c = 1 . 5 X 10^ cms. per second. 



The maximum energies transmissible would depend on the depth 

 at which transmission takes place, for the static pressure will increase 

 as the depth increases. If P is the atmospheric pressure and d the 

 d^pth, the maximum energy transmissible per sq. cm. per sec. 



_ , {P+pdY 



pc 



ergs. 



and the maximum amplitude, at frequency/, = cms. 



2tvJpC 



These formulae and figures indicate clearly that in the case of the 

 transmission of sound through liquids it might occur that cavitation 

 of the kind here discussed would limit the power of transmission, 

 and therefore it would follow that the deeper the radiating source 

 was immersed the greater would be the amount of energy trans- 

 missible. When the maximum of energy transmission at a given 

 depth had been reached, the only means then of increasing the 

 radiating power would be to increase the emitting surface of the 



radiator^ 



^Lamb, Dynamical Theory of Sound, para. 63. 



