A wire is under tension of 2 kg wt and a wave is travelling through it with some speed. Tension in the wire is so increased that the wave travels through it with thrice the original speed. The increase in tension is (in kg wt)

Step-by-step solution

The speed of a transverse wave in a stretched wire is given by v = T where T is the tension and is the linear mass density. Since the speed is proportional to the square root of tension, we have v T Given that the new speed is thrice the original speed, v₂ = 3v₁ T₂ = 3 T₁ T₂ = 9T₁ Given the initial tension T₁ = 2 kg wt, the new tension is T₂ = 9 2 = 18 kg wt. The increase in tension is T = T₂ - T₁ = 18 - 2 = 16 kg wt. Answer: 16