Use the following scenario to answer the next question. A rope of length L and linear mass density $\mu$ is tied to the ceiling on one end. The other end is tied to a spring with spring constant k, and the spring is then attached to the floor, extending it by A.
-The time it takes for a wave pulse to travel from the bottom of the rope to the ceiling is

Question

Quizplus · Accepted Answer

The wave speed v is given by v=sqrt(T/μ), where T is the tension in the rope and μ is the linear mass density. Tension is given by T=F1g, where F1 is the force hanging from the rope, and g is the acceleration due to gravity. Therefore, T=F1gL. The force F1 is given by F1=kA, where A is the displacement of the spring. Therefore, T=kALg. The wave speed is then v=sqrt(kALg/μ). The time it takes for a wave pulse to travel from the floor to the ceiling is given by t=L/v. Substituting the expression for v, we get t=L/sqrt(kgL/μ), which simplifies to t=sqrt(L/kμ). Therefore, the answer is B.

Use the Following Scenario to Answer the Next Question μ\muμ Is Tied to the Ceiling on One End

Use the Following Scenario to Answer the Next Question $\mu$ Is Tied to the Ceiling on One End