ON THE PROPAGATION OF LONGITUDINAL WAVES IN CYLINDRICAL RODS

Abstract

The solution of the velocity equation obtained by Pochhammer on the basis of the mathematical theory of elasticity is determined for the propagation of longitudinal waves of any frequency in a long solid circular cylinder of any diameter. For a given frequency a large number of solutions may be obtained, but when the condition is imposed that for low frequencies the velocity must gradually assume the value found by experiment, a single value is obtained for each frequency. The velocity decreases with increasing frequency, so that, for a cylinder of finite length, the resonance frequencies come closer and closer together. It is also necessary to take into account, however, that in a solid rod longitudinal waves are accompanied by radial vibrations of the particles, and that a cylindrical rod has, regardless of its length, a series of natural frequencies for radial waves, so that for wave-lengths comparable with the diameter of the tube a coupled system of oscillations is set up. The resonant frequencies of such a system depend on the degree of coupling.