Calculate the wavelength of the resulting wave on the cable. (Answer in meters)

Question

A steel cable with total length 38m and mass 130kg is connected to two poles. The tension in the cable is 2,242 N, and the wind makes the cable vibrate with a frequency of 2 Hz. 

Answer 1

Hi Victoria,

I'm sure you're aware of the general wave equation, v = f *λ, where λ is the wavelength. Ultimately, you will want to use this formula, but you need to find the speed first - that's the hard part.

One formula for speed of a wave in a cable/rope is: v = √(T/μ), where T is tension, and μ is something called the linear mass density - which is basically measuring how heavy the rope is per meter: μ = m/L

So, this is really a 3-step problem:

1) Find μ, the linear mass density of the rope

2) Use that to find the speed of the wave

3) Use that to find the wavelength