When is a Pepsi® can more than just a beverage container? When it is the inspiration for an acoustics homework problem!

Abstract

When teaching acoustics to graduate students, some of most effective homework problems require students to compare multiples approaches, combine concepts from related topics, and evaluate numerical answers using experimental data. A problem from David T. Blackstock’s Fundamentals of Physical Acoustics textbook asks students to model an empty beverage can as a Helmholtz resonator, first using the simple formula and the measured dimensions of a real can. Then, students are asked to evaluate whether the simple formula is valid and to provide a more accurate solution if it is not. Most students find an improved impedance approach solution which changes the calculated frequency by approximately 9%. However, most students fail to realize that this problem is exactly analogous to the problem of elastic longitudinal waves in a fixed, mass-loaded bar, with the related first approximation of a simple mass-spring system in which 1/3 of the spring’s mass must be included. Further challenges arise when students attempt to measure the resonance of the empty can and obtain a measured frequency (with damping) that does not match calculated values. The pop-can resonator problem, its analogues, and some experimental challenges will be discussed in detail.