All Problems Elastic Waves. Acoustics.
Problem 4.172
A string of mass \(m\) is fixed at both ends. The fundamental tone oscillations are excited with circular frequency \(\omega\) and maximum displacement amplitude \(a_{\max } .\) Find: (a) the maximum kinetic energy of the string; (b) the mean kinetic energy of the string averaged over one oscillation period.
(a) \(T_{\max }=1 / 4 m \omega^{2} a_{\max }^{2} ;\) (b) \(\langle T\rangle=1 /{ }_{8} m \omega^{2} a_{\max }^{2}\)