Vibrations problem - Transverse in a string under tension

AI Thread Summary
The discussion centers on deriving the equation for natural frequencies of a cord under tension, specifically showing that tan(wL/c) = -(T/kL)((wL/c)/(1-(w/w_n)^2)). Key equations include w_n^2 = k/m and c^2 = T/(pS), which relate to the tension and density of the cord. Participants express difficulty in starting the problem and question the correctness of the provided equation. The natural frequencies are noted to be determined by the relationship f = v/lambda, where v is the wave speed. The conversation emphasizes the need for clarity in the derivation process and understanding the physical principles involved.
alexisonsmith
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Homework Statement


A cord of length L density p and cross-sectional area S is under tension T with the left end fixed and the right end attached to a spring-mass sstem. Show that the equation for the natural frequencies is given by:

tan(wL/c) = -(T/kL)((wL/c)/(1-(w/w_n)^2))


Homework Equations



w_n^2 = k/m and c^2 = T/(pS)

The Attempt at a Solution



I have tried this but I am really having problems starting this problem out, please help
 
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Are you sure that equation is right? The natural frequencies are given very simply by f=v/lambda, where v^2=c^2 = T/(pS) and lambda is a half-integer multiple of the pipe's length.
 
Yes it is Q.2 on the sheet which I have attached.
 

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