Abstract:
Schrodinger equation in quantum mechanica has similar mathematical strueture as clanaical woves, in foet, the time-independent versions of the two can be identicatin certain cases leading to the same spatial solutione for the two cases Such a common ergen-mode solution ceschbes the specine eigne-energy for the quantum state and eigen-trequency tor the classical wave. Thus the phenomena common in quantummechanics, euch as avoided crossings or Fand interference, can also be been in classical waves A simple inexpentive erperiment involving the sound modes in a partitioned pipe is uced to demonstrate these phenomena expon montally.

A closed thin-cylindrical pipe is a one-dimensional sound cavity that hot well defined reconant acoustic modies. Such a resonator with a solid partition dita forma two one-dimentional cavitien that have a series of retonant frequencies that depend on the dice pocition. A omall hole in this disc leads to interactions between the two cavities modes, and hence to croidedi crossings infrequency whenever the two frequencies nearly coincide.

tranemittion as a function of frequency through such a pipe and dise arrangement A remarkable agreement in then obtained between the experiment and a simple model bated on sound wave trandmittion and reflection at different interfaces Il. Another concept that the same experiment illustrates is the Fano resonance that leads to an anymmetry in the spectral line-shapes. In this cate, the sound tranamicion through a resonant and a non-resonant broad-mode and subsequent interference leade to a similar atymmetric lina shape. view poster...