THEORETICAL AND EXPERIMENTAL MODELING AND STUDY OF COMPRESSIONAL WAVE MOTION IN PERIODICAL STRUCTURES
Pages 142-150
Ioan Cosma, Diana I. Popescu
Abstract
Our work presents a theoretical model and an original experimental method addressed to our eye and brain for
understand what is happening to each and every particles that compose a periodical structure when is set into
longitudinal oscillations, and to see how the same kind of analysis applies to a system of particles connected
by springs along a straight limited line. Physical and mathematical considerations allow us to establish the
differential equation and characteristics of compressional traveling waves in helix springs. The
particularization of these, for the limited pseudo-continuous medium, gives the time independent wave
equation that, by its eigensolutions, can describe not only the standing waves, but also the multiple resonances
and normal modes of vibration in this macroscopic periodical structure, as well as in crystalline materials,
along a domain selected direction of the lattice. Our experimental method for visual observation and
quantitative study of wave motion became possible trough the use of a long helical spring, stretched in vertical
position that is excited at its lower end by an electromagnetic audio-vibrator. Obtained results on long helix
springs and on beds rubber strings are agree with the theoretical model, being a convincing experiment for
perceiving the intricate widespread phenomenon of sound waves that exist in solids, liquids and gases, but that
are directly invisible.