String Tension

The tension of a vibrating string is the force used to stretch it. It is therefore directed along the axis of the string. A force must be applied at the endpoint on the right, and a force is applied at the endpoint on the left. Each point interior to the string is pulled equally to the left and right, i.e., the net force on an interior point is . (A nonzero force on a massless point would produce an infinite acceleration.)

If the cross-sectional area of the string is , then the tension is given by the stress on the string times .

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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.