A transverse wave described by Y = (0.02 m) sin [(1.0 m-1) x + (30 s-1)t] Propagates on a stretched string having a linear mass density of 1.2 × 10-4 kg m-1. Find the tension in the string.

Sol. . m = mass per unit length = 1.2 * 10–4 kg/mt Y = (0.02m) sin [(1.0 m–1)x + (30 s–1)t] Here, k = 1 m–1 = 2π/λ ω = 30 s–1 = 2πf ∴ velocity of the wave in the stretched string v = λf = ω/k = 30/I = 30 m/s ⇒ v = √T /m ⇒ 30 √(T /1.2) *10-4N) ⇒ T = 10.8 * 10–2 N ⇒ T = 1.08 * 10–1 Newton.