MODELLING THE DISPERSION PROPERTIES OF MASS LINEAR CHAINS: EXPERIMENTS AND SIMULATIONS

We analyze and discuss the results of an experiment with the goal of revealing the phonon-like acoustic dispersion curve. The experimental apparatus consists of a sonometer and an electromagnetic driver connected to a signal generator in order to establish standing waves along a stretched metal string (a guitar string) upon which a set of beads (used normally for fishing) has been fixed. The oscillation amplitude is measured by means of a detector connected to an MBL interface. We detect the resonance frequencies as function of the wave-number and obtain the corresponding dispersion curve. The results show that deviations from linearity occur when the wavelength is comparable with the distance between two nearest beads. Measurements are repeated by varying bead mass and with different strings. Comparison with theoretical results is also performed. From a pedagogical point of view the experiment is very simple and allows to introduce some basic concepts in solid state physics as resonance, normal modes, dispersion and the effect of medium discreteness onto mechanical wave propagation. The modelling phase is also discussed by means of interactive simulations.