The wave equation
for the ideal vibrating string may be written as
 |
(7.1) |
where we define the following notation:
As discussed in Chapter
1, the
wave equation in this form can be
interpreted as a statement of Newton's second law,
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.
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