204 t6 



The bubbles make the water effectively much more compressible, 

 hence the velocity of propagation will be greatly reduced. An isolated pulse 

 of pressure may, for this reason, be retarded in its passage through the bub- 

 bly water. 



Furthermore, if there is a definite boundary between the homogene- 

 ous and the bubbly water, partial reflection of the wave may be expected at 

 the boundary. The reflection may, however, be reduced in amount by the oc- 

 currence of cavitation at the boundary of the layer of bubbly water. The 

 wave reflected from the first surface of this layer will necessarily be one 

 of tension, since the bubbles reduce the acoustic impedance of the water. If 

 the v;ater cannot stand the requisite tension, cavitation will occur in the 

 homogeneous water, and in this case the reflected tension wave will be partly 

 or wholly absent. A layer of cavitated water should then advance against the 

 bubbly water, and subsequently move back again; the impact of this layer 

 against other water may give rise to a secondary reflected wave of positive 

 pressure. 



It would be expected that high-pressure waves would be less effec- 

 tively reflected than low-pressure waves. For, if the pressure is great 

 enough to cause the bubbles to collapse almost completely, further increase 

 of pressure will not cause materially greater amplitude of motion of the bub- 

 bles, so that the reflecting action cannot increase in proportion to the in- 

 cident pressure. 



Additional complications, perhaps resembling resonance effects, may 

 result from the inertia of the water surrounding the bubbles. Furthermore, 

 loss of energy due to scattering of the wave by the oscillating bubbles, or 

 to other causes, will result in a weakening of the wave. 



Because of these effects, the bubbly water will behave as a disper- 

 sive, absorbing medium. The dispersive action, signifying that the various 

 harmonic components of the wave travel at different speeds, will cause the 

 wave to Increase in length as it passes through the bubbly layer. If the du- 

 ration of the wave is short enough relative to the time of vibration of the 

 bubbles, the lengthening may be so great that it is best described as a re- 

 emission of pressure by the compressed bubbles as they expand again. 



The wave of pressure that emerges on the far side of the layer of 

 bubbles will thus be likely to be weaker but of longer duration than the 

 original incident wave. There are, furthermore, other effects that lengthen 

 the transmitted wave. Repeated reflections from the boundaries of the layer 

 may occur. A single entering pulse may thus emerge as a series of repeated 

 pulses of rapidly diminishing amplitude, which will blend together more or 

 less completely into a transmitted wave of increased length. 



