You hold one end of a horizontal string and raise your hand during a time interval of 0.18 s, doing 3.1 J of work on the string in the process. You then allow your hand to return to its original position.

If the wave pulse you create travels along the string at 55 m/s and the linear mass density of the string is 0.0282 kg/m , what was the vertical speed of your hand?

v =