A crane lifts a 2500-kg beam at a steady rate of 15 cm/s using a steel cable whose mass per unit length is 0.65 kg/m. What is the speed of transverse waves on this cable?
A) 190 m/s
B) 580 m/s
C) 1900 m/s
D) 230 m/s
E) 1200 m/s

Question

Quizplus · Accepted Answer

The speed of transverse waves on a string or cable is given by $v = \sqrt{\frac{T}{\mu}}$, where $T$ is the tension in the cable and $\mu$ is the mass per unit length. The tension $T$ is equal to the weight of the beam, which is $mg = 2500 \times 9.8 = 24500 \, \text{N}$. The mass per unit length $\mu = 0.65 \, \text{kg/m}$. Substituting these values into the formula gives $v = \sqrt{\frac{24500}{0.65}} \approx 190 \, \text{m/s}$.

A Crane Lifts a 2500-Kg Beam at a Steady Rate