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The wave equation for the ideal vibrating string may be written as
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on a microscopic scale. Since we are concerned with transverse vibrations on the string, the relevant restoring force (per unit length) is given by the string tension (force along the string axis) times the curvature of the string, or
; the restoring
force is balanced at all times by the inertial force per unit length
of the string which is equal to mass density (mass per unit length)
times transverse acceleration, i.e.,
. See Appendix B
for a review of basic physical concepts. The wave equation is derived
in some detail in §B.6.
