The screening of sound in a subsonic flow by a cylindrical airbubble layer and a semi-infinite tube

The problem here under discussion lies in the field of sound waves in layered media. The presence of a layer with a velocity of sound less than that of the surroundings will enable sound waves to travel along great distances. In this domain many investigations have been made e. g. in connection with the propagation of sound in the ocean. Sound velocity in sea-water is a function of depth and reaches a minimum at approximately 1 kilometer under the surface of the sea. It is this minimum that sees to it that waves starting on this level can stay approximately at this level. In this way sound waves can travel over great distances on a depth which is almost exclusively limited to the direct neighbourhood of this minimum and that is why one is speaking of a sound channel. For the analogous rotational problem Sparenberg has examined the existence of such waves. From the general problem we deduce several particular cases. In chapter XIX we suppose the source is placed far inside the rigid tube and in chapter XX the source is situated far outside the tube. In chapter XXI we examine the case without a bubble screen. The problem without a semi-infinite tube is treated in for the special case that the undisturbed media are at rest, hence U=O. Chapter XXII gives for this case the most important formulae when the media have a subsonic velocity U. (see file, Le grand the screening of sound)... Zie: Introductio