15.53: a) See Exercise 15.10; ,222yωatyy-==∂∂and so .22ωxμmωk∆=∆=′b) (2922222422μλFπλπvπfω===and so .)4(22xFπk∆λ=′The effective force constant k′is independent of amplitude, as for a simple harmonic oscillator, and is proportional to the tension that provides the restoring force. The factor of 21λindicates that the curvature of the string creates the restoring force on a segment of the string. More specifically, one factor of
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