188 



TABLE OP CONTENTS 



Page 



ABSTRACT 1 



INTRODUCTION ^ 



PERIOD OF OSCILLATION 2 



TIME-DISPLACEMENT CURVES ^ 



PRESSURE IN THE WATER 5 



RADIATION OF ENERGY 9 



A PRESSURE WAVE AND A GAS BUBBLE Tl 



SLOWLY VARYING PRESSURE 12 



IMPULSIVE PRESSURE 1^ 



THE GENERAL CASE 1 5 



A PRESSURE WAVE INCIDENT ON BUBBLY WATER 15 



WEAK SINUSOIDAL WAVES IN FINE-GRAINED BUBBLY WATER I? 



REFERENCES ^^ 



APPENDIX 



MATHEMATICAL THEORY OF RADIAL MOTION 

 AROUND GAS SPHERES IN WATER 



THE RADIAL MOTION 24 



PRESSURE IN THE WATER 26 



RADIATION OF ENERGY 28 



BUBBLE UNDER VARIABLE EXTERNAL PRESSURE 50 



EFFECT OF MANY SMALL BUBBLES ON LONG PLANE 



SINUSOIDAL WAVES OF A SMALL AMPLITUDE • ^' 



COEFFICIENT OF REFLECTION 5^ 



SCATTERING BY A SINGLE BUBBLE , . . . 37 



