Abstract
A marimba bar makes a rich and vibrant sound when played by a skilled musician. When that same marimba bar is played by the typical mechanical engineering junior, it’s a different story. Then, that same marimba key provides a complex set of vibration modes that are a useful subject for a lab experiment in their Measurements & Instrumentation course. This paper will describe development of “The Marimba Experiment”, which is part of a junior-level engineering course in measurements at Milwaukee School of Engineering. Learning outcomes for this course include “provide students with hands-on experience: using various sensors, performing data collection, and interpretation of experimental results.” In this experiment, students measure vibrations using a piezoelectric accelerometer, charge amplifier and analog-to-digital conversion. Results can be viewed in two ways. First, it may be interpreted as a general example of a vibrating structural component. It has several natural frequencies and mode shapes (transverse bending, lateral bending, torsional), which are simultaneously active. The signal represents an example of a complex periodic signal. It may be analyzed by looking at the acceleration versus time response and by examining the Fourier transform of the data, which shows results in the frequency domain. Second, results may be interpreted in musical terms. The lowest frequency is what we recognize as “the note” and the higher modes represent the higher harmonics. The distribution of frequency ratios and the relative amplitudes of the higher frequencies are what gives a musical instrument its unique character. In other words, what makes middle-C on a marimba sound different than middle-C on a clarinet or violin? A well-designed engineering experiment can give students an immediate application example. In this case, it is an example which they spontaneously want to explore because they all enjoy music and want to understand how it is created.
