Two ropes, A and B, are tied and stretched. Rope A has a linear mass density 9 times higher than rope B. A pulse travels in rope A and continues in B. The speed of the pulse in rope A is v_A, and in rope B it is v_B. What is the relationship between the speeds? A)v_B = 9v_A B)v_B = 3v_A C)v_A = 9v_B D)v_A = 3v_B

Question

Quizplus · Accepted Answer

The speed of a pulse in a stretched rope is given by v = sqrt(T/μ), where T is the tension in the rope and μ is the linear mass density. Since the tension is the same in both ropes, the ratio of the speeds is vA/vB = sqrt(μB/μA) = sqrt(1/9) = 1/3. Therefore, vB = 3vA.

Two Ropes, a and B, Are Tied and Stretched