Unformatted text preview: ) 2 ( 2 L mω C = and the previous result is obtained. The speed of propagation as a function of distance is , 2 ) ( ) ( 2 2 r L ω m TL μ r T dt dr r v= = = = where dt dr has been chosen for a wave traveling from the center to the edge. Separating variables and integrating, the time t is . 2 2 2 ∫ ∫= = L r L dr ω dt t The integral may be found in a table, or in Appendix B. The integral is done explicitly by letting , cos , cos , sin 2 2 θ L r L dθ θ L dr θ L r == = so that . 2 arcsin(1) 2 and , arcsin 2 2 ω π ω t L r θ r L dr = = = =∫...
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 Calculus, Force, Dr T, edge. dt

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