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 a 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 .
Damped Traveling Waves
A Software Delay Line