Traveling Waves

In acoustic wave propagation, pure delays can be used to simulate traveling waves. A traveling wave is any kind of wave which propagates in a single direction with negligible change in shape. An important class of traveling waves is ``plane waves'' in air which create ``standing waves'' in rectangular enclosures such as ``shoebox'' shaped concert halls. Also, far away from any acoustic source (where ``far'' is defined as ``many wavelengths''), the direct sound emanating from any source can be well approximated as a plane wave, and thus as an ideal traveling wave.

Another case in which plane waves dominate is the cylindrical bore, such as the bore of a clarinet or the straight tube segments of a trumpet. Additionally, the vocal tract is generally simulated using plane waves, though in this instance there is a higher degree of approximation error.

Transverse and longitudinal waves in a vibrating string, such as on a guitar, are also nearly perfect traveling waves, and they can be simulated to a very high degree of perceptual accuracy by approximating them as ideal, while implementing slight losses and dispersion once per period (i.e., at one particular point along the ``virtual string'').

In a conical bore, we find sections of spherical waves taking the place of plane waves. However, they still ``travel'' like plane waves, and we can still use a delay line to simulate their propagation. The same applies to spherical waves created by a ``point source.'' Spherical waves will be considered on page .

---

Order a Hardcopy of Physical Audio Signal Processing

Previous: Acoustic Wave Propagation Simulation
Next: Damped Traveling Waves

---

written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.