1. Determine the relationship of the fundamental frequency of a vibrating string to the mass per unit length, the length of the string, and the tension in the string.
2. If, for a vibrating wire, the original displacement of the 2- m-long stationary wire is given by
(a) 0.1 sin x π/2,
(b) 0.1 sin 3πx/2, and
(c) 0.1(sin πx/2 - sin 3πx/2), find the displacement function u(x,t). Both ends are fixed, P = 50 N, and the mass per unit length is 0.01 kg/m. With what frequency does the wire oscillate? Write the eigenvalue and eigenfunction for part (a).