Serway & Jewett — Wave Motion: Problem 49

A wire of density \(\rho\) is tapered so that its cross-sectional area varies with \(x\) according to \[A = 1.00 \times 10^{-5}x + 1.00 \times 10^{-6}\] where \(A\) is in meters squared and \(x\) is in meters. The tension in the wire is \(T\). (a) Derive a relationship for the speed of a wave as a function of position. (b) What If? Assume the wire is aluminum and is under a tension \(T = 24.0 \text{ N}\). Determine the wave speed at the origin and at \(x = 10.0 \text{ m}\).