10. Consider a block of mass Mhanging at rest from a cable of length L and mass density . The cable is plucked at the bottom, and a wave pulse propagates up the cable to the top, where it is attached to the ceiling. (a) If the mass of the cable is negligible compared to M(ie. the tension is uniform throughout the cable), show that the travel time for the pulse is: (b) t = L Mg Now consider the case when the mass of the cable is not negligible, so that the tension varies with position. Show that the travel time is: M L t = 2 1+ 1 M and verify that, in the limit 0, you recover the answer from part (a). Hint: find the tension as a function of distance x from the bottom of the cable. Express the infinitesmal time dt in terms of an infinitesmal distance up the cable dx and the instantaneous speed v, which will vary with x due to the variation of tension. Integrate to find t. (1+x) 1+nx (binomial approximation)