Transmission of Sound in a Liquid between Concentric cylinders Free

The theoretical work of W. J. Jacobi on the propagation of sound waves along liquid cylinders has been extended to the case of sound transmission through a liquid bounded by two concentric cylinder of infinite length. Longitudinal phase velocities and radial distributions of pressure amplitude have been calculated, and the form of the Fourier‐Bessel expansion coefficients has been worked out for rigid, pressure‐release, and elastic wall boundary conditions. Similar calculations for the case of a single liquid filled cylinder have been made for comparison. The case of two concentric cylinders approaches that of a single cylinder as the radius of the inner cylinder approaches zero. Experimental values of phase velocity have been determined for the case of two finite concentric cylinders with elastic walls and are in good agreement with theory over parts of the range from 3 to 200 kc.