A transverse wave on a stretched string is described by the equation y(x,t) = 0.05 (40x - 800t) , where x and y are in metres and t is in seconds. If the linear mass density of the string is 5.0 ~g/m , the tension in the string is :

Step-by-step solution

Comparing the given wave equation y(x,t) = 0.05 (40x - 800t) with the standard form y(x,t) = A (kx - t) , we get: Angular frequency, = 800 ~rad/s Wave number, k = 40 ~rad/m The wave speed v is given by: v = k = 800 40 = 20 ~m/s The linear mass density of the string is: = 5.0 ~g/m = 5.0 10⁻³ ~kg/m The speed of a transverse wave on a stretched string is related to the tension T by: v = T Squaring both sides and solving for T : T = v² T = (5.0 10⁻³) (20)² T = 5.0 10⁻³ 400 = 2 ~N Answer: 2 ~N