Abstract:

Musical acoustics provides attractive examples that can be used to introduce engineering majors and nonmajors alike to critical concepts in engineering practice. Foremost among these is the concept of the eigenmodes and accompanying eigenfrequencies of a linear system. These can be wonderfully demonstrated via analysis of the overtone series of brass instruments (a one-dimensional system) and circular drumhead vibrations (a two-dimensional system). As an added bonus, important practical engineering concepts can be explored with these systems, such as the effect of nonlinearities and of nonideal properties on system behavior. Other natural topics include impedance, regenerative feedback, modal coupling, and frequency-dependent boundary conditions. [Work supported by NSF.]