The tension in a 3.4 m long,1.0-cm diameter steel cable ( )under 480 N.What is the fundamental frequency of vibration of the cable?

Question

The tension in a 3.4 m long,1.0-cm diameter steel cable (  )under 480 N.What is the fundamental frequency of vibration of the cable?

Quizplus · Accepted Answer

The fundamental frequency of vibration for a cable is given by:
f = (1/2L) * sqrt(Tension/mass per unit length)
where L is the length of the cable, Tension is the tension force applied on the cable, and mass per unit length is the linear density of the cable.
The linear density of steel is about 7850 kg/m^3. Thus, the mass per unit length of the cable is:
mass per unit length = (pi/4) * diameter^2 * 7850
= (pi/4) * 0.01^2 * 7850
= 0.0194 kg/m
Substituting the given values, we get:
f = (1/2*3.4) * sqrt(480/0.0194)
= 2.1 Hz (approx)
Therefore, the correct answer is (C) 2.1 Hz.

The Tension in a 3