On the Radiation Impedance of the Liquid-Filled Squirting Cylinder

The impedance presented to the inside surface of a hollow, radially vibrating, liquid-filled cylinder of length ℓ which is mounted in the aperture of a rigid wall of thickness ℓ has been determined. It was assumed that radiation from the ends of the cylinder into the infinite liquid media (water) takes place symmetrically with respect to the plane midway between the ends of the cylinder. The liquid within the cylinder need not be the same as the liquid outside the cylinder. Although the impedance at any frequency can be obtained from the results, an approximation is introduced which is valid when the wavelength in the liquid within the cylinder is such that ka⩽π/2 (k being the wavelength constant and a the inside radius of the cylinder). Under these circumstances it is found that the output power drops to zero whenever the length of the cylinder equals nλ, where n is an integer and λ is the wavelength of sound in the contained liquid.