The glissando of colliding hard objects
Benjamin Frey, William M. Hartmann · The Journal of the Acoustical Society of America · 2004
When two hard objects are pressed together they alternately collide and rebound, leading to an audible, decaying sequence of pulses with a decreasing interpulse interval. Therefore, the sequence is heard as a rising pitch or glissando. Virtuoso performances of colliding hard objects (steel spheres) demonstrated a frequency rise that was accurately an exponential function of time over the span of more than three octaves. The amplitude decay also tended to be exponential, though less reproducibly so. Because successive decaying pulses were otherwise virtually identical functions of time, the spectra were harmonic. Four harmonics were clearly evident in spectrograms. Spectrograms also revealed a strong formant near 2000 Hz, presumably indicating the lowest mode of vibration of the steel spheres themselves. Formants had a Q of about 7. With the quantitative acoustical description well in hand, interest now centers on discovering the time-dependent force function employed by experienced performers of colliding hard objects when they achieve the most effective glissandos. [Work supported by the Michigan State University Professorial Assistant Program.]