The linear mass density of a nonuniform wire under constant tension decreases gradually along the wire so that an incident wave is transmitted without reflection. The wire is uniform for – ∞ ≤ x ≤ 0. In this region, a transverse wave has the form y(x, t) = 0.003 cos (25x – 50t), where y and x are in meters and t is in seconds. From x = 0 to x = 20 m, the linear mass density decreases gradually from μ₁ to μ₁/4. For 20 ≤ x ≤ ∞, the linear mass density is μ = μ₁/4.

(a) Find the wave velocity for large values of x.

(b) Find the amplitude of the wave for large values of x.

(c) Give y(x, t) for 20 ≤ x ≤ ∞.