How Much Tension Is Needed in a Rope for Specific Wave Properties?

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To determine the required tension in a rope for transverse waves of a specific frequency and wavelength, the wave number K is calculated as K = (2*Pi)/0.750, resulting in K = 8.38 1/m. The next step involves using the wave speed formula v = √(T/μ), where μ is the mass per unit length of the rope. Given the rope's mass of 0.120 kg and length of 5 m, μ is calculated as 0.024 kg/m. The relationship between wave speed, frequency, and wavelength can then be used to find the necessary tension T for the desired wave properties. Understanding these calculations is crucial for solving the problem effectively.
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Homework Statement


With what tension must a rope with length 5m, and mass 0.120 kg, be stretched for transverse waves of frequency 50.0 Hz to have a wavelength of 0.750 m?


Homework Equations


K = ((2*Pi)/wavelength)


The Attempt at a Solution


K = (2*Pi)/.75
K = 8.38 1/m

I'm not sure where to go from here.
 
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Use the following relationship: v = √(T/μ).

v is the speed of the waves, T is the tension, and μ is the mass per unit length.
 

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