A heavy rope 6.00 m long and weighing 29.4 N is attached at one end to a ceiling and hangs vertically. A 0.500 kg mass is suspended from the lower end of the rope.

a) What is the speed of transverse waves on the rope at the bottom of the rope?
b) What is the speed of transverse waves on the rope at the middle of the rope?
c) What is the speed of transverse waves on the rope at the top of the rope?
d) Is the tension in the middle of the rope the average of the tensions at the top and bottom of the rope? Is the wave speed at the middle of the rope the average of the wave speeds at the top and bottom? Select the correct answer and explanation.

A. The tension at the middle is the average of the top and bottom tensions, and the speed at the middle is the average of the top and bottom speeds because the speed is proportional to the tension.
B. The speed at the middle is the average of the top and bottom speeds, but the average tension is not equal to the tension at the middle because the tension depends on the square root of the speed.
C. The speed at the middle is not equal to the average speed, and the average tension is not equal to the tension at the middle because the tension is proportional to the speed.
D. The tension at the middle is the average of the top and bottom tensions, but the average speed is not equal to the speed at the middle because the speed depends on the square root of the tension.