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**[SOLVED] Transverse Wave on a Hanging Cord**

**Problem.**A uniform cord of length L and mass m is hung vertically from a support.

**(a)**Show that the speed of tranverse waves in this cord is [itex]\sqrt{gh}[/itex] where h is the height above the lower end.

**(b)**How long does it take for a pulse to travel upward from one end to the other?

For (a), I know that the speed of a transverse wave on a cord is given by [itex]v = \sqrt{T/\mu}[/itex] where T is the tension on the cord and [itex]\mu[/itex] is the linear density. As far as I understand, T = mg and [itex]\mu = m/L[/itex] so [itex]v = \sqrt{gL}[/itex]. Now, unless h = L (which I know isn't), I don't see how h plays a role here.

The answer to (b) is just L/v obviously.