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

[Jim4592]

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.

 

[dx]

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.

 

[nlightner]

I would approach this problem by first identifying the relevant equations and principles that can help us calculate the tension in the rope. In this case, we can use the equation T = (m/L) * (w^2 * L), where T is the tension in the rope, m is the mass of the rope, L is the length of the rope, and w is the angular frequency of the wave.

Using the given values, we can plug in the numbers and solve for the tension:
T = (0.120 kg / 5m) * (50.0 Hz)^2 * 0.750m
T = 45 N

Therefore, the tension in the rope must be 45 N for the transverse waves to have a wavelength of 0.750 m. It is important to note that this calculation assumes that the rope is perfectly elastic and does not have any other forces acting on it. In real-world situations, there may be other factors that can affect the tension in the rope.