The equation of a wave on a string of linear mass density 0.02 kg m ⁻¹ is Y = 0.01 [2 ( t 0.02 - x 0.50 ) ] m. The tension in the string is

Step-by-step solution

The given wave equation is Y = 0.01 [2 ( t 0.02 - x 0.50 ) ] m. Comparing this with the standard wave equation Y = A ( t - kx) , we get: = 2 0.02 = 100 rad s ⁻¹ k = 2 0.50 = 4 m ⁻¹ The wave velocity v is given by: v = k = 100 4 = 25 m s ⁻¹ The velocity of a transverse wave on a string is also given by v = T , where T is the tension and is the linear mass density. Given = 0.02 kg m ⁻¹ . T = v^2 = 0.02 (25)^2 T = 0.02 625 = 12.50 N Answer: 12.50 N