Longitudinal Wave Transmission and Impact

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Abstract
When a force is applied to a body, waves of stress and velocity radiate through the body from the point of application of the force. When these waves strike the boundaries of the body they may be wholly or partially transmitted to surrounding bodies or reflected back into the body, where they may reverberate back and forth within its confines, like sound waves within the body of air in a closed room. By superposition of these radiated and reflected waves the stress and motion of all parts of the body are gradually, and in general discontinuously, brought up to the values ordinarily assumed. In the case of a small body this whole process takes place so quickly that there is great difficulty in detecting it, and generally it is of little practical importance. But there are cases where it is desirable to study the process in detail, particularly when the dimensions to be dealt with are no longer very small compared to the velocities of such waves, and in consequence the time element is no longer negligible, or where the time of application or variation of applied forces is very small and hence of the same order of magnitude as the aforementioned time element, as in cases of impact or harmonic forces of considerable frequency. In the present paper an attempt is made to consider some of the more important phases of this subject in as simple a manner as possible.

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