Longitudinal Waves

In addition to transverse waves on a string, there are always longitudinal waves present as well. In fact, longitudinal waves hold all of the potential energy associated with the transverse waves, and they carry the forward momentum in the direction of propagation associated with transverse traveling waves [121]. Longitudinal waves in a string typically travel an order of magnitude faster than transverse waves on the same string and are only weakly affected by changes in string tension.

Longitudinal waves are often neglected, e.g., in violin acoustics, because they couple inefficiently to the body through the bridge, and because they are ``out of tune'' anyway. However, there exist stringed instruments, such as the Finnish Kantele [234], in which longitudinal waves are too important to neglect. In the piano, longitudinal waves are quite audible; to bring this out in a striking way, sound example 5 provided in [22, Conklin chapter] plays Yankee Doodle on the longitudinal modes of three piano strings all tuned to the same (transversal) pitch.

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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.