Calculate the wavelength of the resulting wave on the cable.

Question

A steel cable with total length 68 m and mass 150 kg is connected to two poles. The tension in the cable is 2,039 N, and the wind makes the cable vibrate with a frequency of 2 Hz. Calculate the wavelength of the resulting wave on the cable.

Answer 1

Hello, Emma!

You can solve for the wavelength using these two formulas:

1. wavelenth=v/ƒ
2. v=sqrt(Tension/(mass/length))

So we need to find the speed of the wave in order to find the wavelength. We can use the 2. formula listed above to find this because we have tension, mass, and length.

V=sqrt(2039N/(150kg/68m)) =30.4 m/s

Now we can find wavelength using 1. formula listed above.

wavelength=(30.4 m/s)/(2Hz)= 15.2m

So the resulting wavelength is 15.2 meters long.