Empty soft-drink cans and mass-loaded rods: Analogous homework problems from acoustic and mechanical domains

While analogs between electrical, mechanical, and acoustical systems are well known, especially for the analysis of transducers, students encountering analogous acoustical and mechanical systems in different settings often do not recognize the similarities between the systems and their solutions. This paper explores two homework problems that are direct analogs of each other. One problem involves a cylindrical Helmholtz resonator, and the other involves a longitudinal oscillation of a fixed, mass-loaded rod. A detailed analysis of both problems, including lumped-element approximate solutions and more accurate solutions utilizing impedance and boundary conditions, illustrates that these two systems represent essentially the same problem.