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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.

Respuesta :

Answer:

Wavelength = 0.143 m

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 :

[tex]v=\dfrac{\sqrt{\dfrac{T}{m/L}}}{2L}[/tex]

Put all the values,

[tex]v=\dfrac{\sqrt{\dfrac{2222}{140/48}}}{2(48)}\\\\=0.287\ m/s[/tex]

Let the wavelength is [tex]\lambda[/tex]. We know that,

[tex]\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{0.287}{2}\\\\=0.143\ m[/tex]

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

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