Question

A steel cable with total length 48 m and mass 140 kg is connected to two poles. The tension in the cable is 2,222 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

Wavelength = 0.143 m

Step-by-step explanation:

Given that,

The length of a cable, l = 48 m

Mas of the object, m = 140 jg

The tension in the cable, T = 2222 N

The frequency of the cable, f = 2 Hz

We need to find the wavelength of the resulting wave on the cable.The speed of a wave in the string is given by :

`v=\frac{\sqrt{(T)/(m/L)}}{2L}`

Put all the values,

`v=\frac{\sqrt{(2222)/(140/48)}}{2(48)}\\\\=0.287\ m/s`

Let the wavelength is
`\lambda`. We know that,

`\lambda=(v)/(f)\\\\\lambda=(0.287)/(2)\\\\=0.143\ m`

So, the wavelength of the resulting wave is 0.143 m.