The physicist’s guide to the orchestra

An experimental study of strings, woodwind (organ pipe, flute, clarinet, saxophone and recorder) and the voice was undertaken to illustrate the basic principles of sound production in musical instruments. The setup used is simple and consists of common laboratory equipment. The canonical examples (standing wave on a string, in an open and closed pipe) are easily reproduced. The characteristics of the instruments are outlined and discussed. Introduction Being a clarinet enthusiast, I wanted to share the richness of music (and the physicist’s way of approaching it) to engineering students within the frame of their general physics classes. The basics are reported in nearly every physics textbook and many details are provided in more specialized contributions [1–8]. I could not, however, find a comparison of the waveforms and spectra of different instruments in any of these sources. I thus decided to directly measure and compare these data. The whole orchestra being too ambitious for a start, I restricted myself to two instrument families, namely strings and woodwind (the former are given a rather perfunctory treatment), and included the voice. The waveform and spectra presented in the first part illustrate the behaviour of standing waves on strings and in closed and open pipes (variations 1–2), and highlight the basic differences between the timbre of the instruments (variations 3–5). In the second part, we will note that the differences in timbre between instruments are reflected by the measurements, but that variations between models or performers remain hard to assess (variation 6). The characteristics of some instruments will be adressed in more detail (variations 6–8). Theme Physicists have been studying the spectrum of musical instruments at least since the 1940s. The first available methods were based on heterodyne analysis [9] or on sonographs [1, 10]. The development of the fast Fourier transform (FFT) algorithm coupled with the appearance of fast and relatively cheap microprocessors has greatly facilitated the task of musically inclined physicists. Quite sophisticated analysers have been realized [11] but setups based on commercial instruments work just as well for basic analysis [12, 13]. 0143-0807/01/010089+13$30.00 © 2001 IOP Publishing Ltd Printed in the UK 89