With what tension must a rope with length 270 m and mass 013

With what tension must a rope with length 2.70 m and mass 0.135 kg be searched for transverse waves of frequency 36.0 HZ to have a wavelength of 0.700 m ?

Solution

velocity = sqrt(Tension/Linear Density)

Tension = velocity^2 * Linear Density

velocity = frequency * wavelength = (36Hz)(0.70m) = 25.2 m/s

Linear Density = mass / length = 0.135 kg / 2.7 m = 0.05 kg/m

Tension = (25.2)^2 * (0.05 ) = 31.752 N