A string on a musical instrument is held under tension T and extends from the po

Question

A string on a musical instrument is held under tension T and extends from the point x = 0 to the point x = L. The string is overwound with wire in such a way that its mass per unit length ?(x) increases uniformly from ?0 at x = 0 to ?L at x = L. (a) Find an expression for ?(x) as a function of x over the range 0 ? x ? L. (Let ?(0) = ?0 and ?(L) = ?L. Use any variable or symbol stated above along with the following as necessary: x.) ?(x) = (b) Find an expression for the time interval required for a transverse pulse to travel the length of the string. (Use any variable or symbol stated above as necessary.) ?t =

Explanation / Answer

u(x) = u0 + (uL - u0)/L * x

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