Question

A steel cable with total length 83 m and mass 150 kg is connected to two poles. The tension in the cable is 1,968 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

Answer: The wavelength of the resulting wave on the cable is 16.5m

Explanation: Please see the attachments below

Answer 2

The wavelength of the resulting wave on the cable is 16.5 m.

Based on the given information,  

• The length (L) of the steel cable is 83 m.  

• The mass (m) of the steel cable is 150 kg

• The tension (T) in the cable is 1968 N and the wind vibrates the cable at the frequency (f) of 2Hz.  

To calculate the wavelength, first there is a need to find the velocity, which is calculated as,

$Speed of the string wave = V = \sqrt{\frac{TL}{m} }$

$V = \sqrt{\frac{1968N*83m}{150Kg} }$

$V = 32.999 m/s$

The wavelength of the resulting wave is determined as,

$Wavelength = \frac{V}{f}$

$Wavelength = \frac{32.999 m/s}{2 Hz}$

$Wavelength = 16.5 m$

Thus, the wavelength of the resulting wave on the cable is 16.5 m.

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