A steel cable with a total length of 27.7 m and total mass of 91 kg is connected

Question

A steel cable with a total length of 27.7 m and total mass of 91 kg is connected to two poles. The tension in the cable is 869 N and the wind makes the cable vibrate at a frequency of 4.6 Hz. Calculate the wavelength of the resulting wave on the cable. Hint: This is a two part problem where you have to use the length, mass and tension to calculate the velocity of a wave on the cable and then use the velocity to solve the last part of the problem. A steel cable with a total length of 27.7 m and total mass of 91 kg is connected to two poles. The tension in the cable is 869 N and the wind makes the cable vibrate at a frequency of 4.6 Hz. Calculate the wavelength of the resulting wave on the cable. Hint: This is a two part problem where you have to use the length, mass and tension to calculate the velocity of a wave on the cable and then use the velocity to solve the last part of the problem.

Explanation / Answer

velocity in the string is v = √T/μ
velocity = square root (tension / linear density) velcoty v = nλ so λ = v/n = √T/μ * n = velocity = square root(869/(91/27.7))= 16.264 m/s wavelength = (27.7 m/s)/(4.6s^-1) = 6.021739130434783 m

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