A transverse wave is propagating on a stretched string of linear mass density 25 ~g/m . The equation of the wave is given by y(x, t) = 2 (0.1x - 400t) , where x and y are in cm and t is in seconds. The tension in the string is :

Step-by-step solution

Comparing the given wave equation y(x, t) = 2 (0.1x - 400t) with the standard form y(x,t) = A (kx - t) , we identify: k = 0.1 ~cm ⁻¹ = 400 ~rad/s Converting the wave number to standard SI units: k = 0.1 10⁻² ~m ⁻¹ = 10 ~m ⁻¹ The wave speed v is given by: v = k = 400 10 = 40 ~m/s The linear mass density of the string must be converted to kg/m: = 25 ~g/m = 25 10⁻³ ~kg/m The speed of a transverse wave on a stretched string is related to tension T by v = T . Squaring both sides and solving for T : T = v^2 = (25 10⁻³) (