Two uniform ropes, Rope A and Rope B, are knotted together and stretched horizontally under the same tension of 80N. Rope A has linear mass density 0.020kg/m and length 3.0m; Rope B has linear mass density 0.050kg/m and length 4.0m. A single transverse pulse is generated at the free end of Rope A and travels toward the knot, passes into Rope B, and finally reaches a rigid support attached to the far end of Rope B.
(a) Calculate the speed of the pulse in each rope.
(b) Determine the total time it takes the leading crest of the pulse to travel from its point of origin to the rigid support at the far end of Rope B.
(c) After reflecting from the rigid support, the pulse travels back through Rope B and Rope A to its starting point. Calculate the additional time required for this return journey.
(d) Suppose the tension is now adjusted so that the round-trip travel time (origin to rigid support and back) is exactly 0.50s. Keeping the mass densities unchanged, determine the new common tension that achieves this condition.