(Originais Teachy 2023) - Question Very Hard of Physics

A sinusoidal wave travels along a 5.0 m long steel rope. The wave is generated by a device that vibrates the rope at a frequency of 100 Hz. The linear mass of the rope is 0.02 kg/m. Considering the properties of steel (density 7.8 g/cm³ and Young's modulus 200 GPa), calculate: 1) The propagation velocity of the wave in this rope. 2) The tension needed to keep the rope stretched and allow the wave to propagate at the calculated velocity. Remember that the velocity of a transverse wave on a rope is given by V = sqrt(T/μ), where V is the wave velocity, T is the tension in the rope, and μ is the linear mass of the rope. Additionally, the tension in the rope is related to the Young's modulus and the deformation by Hooke's Law, T = Y * (ε * L), where Y is the Young's modulus, ε is the deformation, and L is the initial length of the rope.