An acoustic analog for a quantum mechanical level-splitting route to band formation

Abstract

This paper explores band structure in a simple acoustic apparatus that acts as an analog to the quantum infinite square well with multiple delta-function perturbations. The apparatus can be used to visualize abstract quantum phenomena in a concrete and easily understandable way. It consists of regular sections of PVC pipes connected by variable aluminum diaphragms to allow coupling between the pipe sections. The equivalence between standing waves in the acoustic system and stationary states in the quantum system is examined for multiple-cavity situations. We show that the experimental results from the acoustic system and the analytic solutions of the quantum system demonstrate the same resonance structure. We also experimentally show that the acoustic system supports band structure and that the band width is dependent on the hole size of the diaphragms.