Halliday, Resnick & Walker — Waves-I: Problem 21

21 In Fig. 16-28, an aluminum wire, of length \(L_1 = 60.0 \text{ cm}\), cross-sectional area \(1.25 \times 10^{-2} \text{ cm}^2\), and density \(2.60 \text{ g/cm}^3\), is joined to a steel wire, of density \(7.80 \text{ g/cm}^3\) and the same cross-sectional area. The compound wire, loaded with a block of mass \(m = 10.0 \text{ kg}\), is arranged so that the distance \(L_2\) from the joint to the supporting pulley is \(86.6 \text{ cm}\). Transverse waves are set up on the wire by an external source of variable frequency; a node is located at the pulley. (a) Find the lowest frequency that generates a standing wave having the joint as one of the nodes. (b) How many nodes are observed at this frequency?