A rope of length L and mass M hangs vertically from a ceiling. The tension in the rope is...

A rope of length L and mass M hangs vertically from a ceiling. The tension in the rope is only that due to its own weight, (a) Suppose a wave starts near the bottom of the rope and propaga tes upward. Does the speed of the wave increase, decrease, or stay the same as it moves up the rope? Explain. (b) Show that the speed of waves a height y above the bottom of the rope is .