56 



with common explosives the total acoustic loss of energy 



during the first contracted stage Is never more than a 



fraction ('^25^) of the total energy W of the pulsation, so 



that the correction to the motion Is small to moderate. It 



might therefore be suppose'^ that the radlus-tlme curve could 



be fairly accurately calculated by the methods of Appendix 2. 



However, this does not seem to be the case: the energy loss 



between the first pulsation and the second Is found experimentally ' 



to be much greater than the observed acoustic energy In the 



first bubble pulse. Indicating that some dlsslpatlve mechanism 



Is acting which has not been taken into account in the present 



theory. As an adequate discussion of this question of energy 



balance requires a knowledge of the effects to be expected 



from migration and asymmetry of the bubble, further remarks 



on this point will be postponed until Section 7. 



Let us now consider the way in which the pressure in 

 the acoustic pulse radiate-i by the bubble varies with time. 



This is most conveniently computed in the way suggested by 



18 

 Willis : if a value r-^ of r can be found which is small 



enough so that the relative change of pressure in time r /c 



is small, and which is at the same time large enough so 



that the linear approximation of acoustic theory is valid 



for r>r^ , then the acoustic impulse receive! at any large 



distance r should have an sunplltude given approximately by 



See the article by Willis in this Volume. 



