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Elastic Waves. Acoustics.

Problem 4.172

A string of mass mm is fixed at both ends. The fundamental tone oscillations are excited with circular frequency ω\omega and maximum displacement amplitude amax⁡.a_{\max } . Find: (a) the maximum kinetic energy of the string; (b) the mean kinetic energy of the string averaged over one oscillation period.

Reveal Answer
(a) Tmax⁡=1/4mω2amax⁡2;T_{\max }=1 / 4 m \omega^{2} a_{\max }^{2} ; (b) ⟨T⟩=1/8mω2amax⁡2\langle T\rangle=1 /{ }_{8} m \omega^{2} a_{\max }^{2}
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