Final answer:
The question requires calculating the tension needed in a rope for a specified frequency and wavelength of a transverse wave, which can be found using the wave speed formula and the relationship between wave speed, tension, and linear mass density. The tension in the rope must be 98.84 N.
Step-by-step explanation:
To determine the tension in the rope required for transverse waves of a specific wavelength and frequency, we can use the formula for wave speed: v = √(T/μ), where v is the wave speed, T is the tension in the rope, and μ is the linear mass density of the rope.
Given that the wave speed is v = 41.0 Hz * 0.700 m = 28.7 m/s.
We can rearrange the formula to solve for T: T = v^2 * μ.
Therefore, the tension in the rope must be T = (28.7 m/s)^2 * 0.120 kg/m = 98.84 N.