A long rope with mass ?m is suspended from the ceiling and hangs vertically. A wave pulse is produced at the lower end of the rope, and the pulse travels up the rope. Does the speed of the wave pulse change as it moves up the rope, and if so, does it increase or decrease? Explain.
Solution 15DQ Step 1 of 1: The tension in the rope is not constant. The lower portion of the rope pulls down on the higher portions of the rope. If we imagine that the rope is divided into small segments, we see that the segments near the top of the rope are being pulled down by more weight than the segments near the bottom. Therefore, the tension in the rope increases as we move up the rope. The speed of a transverse wave on the rope is given by v = F /(m / L) . As the tension F in the rope increases, the speed of the wave increases. Therefore, as the transverse wave travels up the rope, the speed of the wave increases.