Bill is making waves on a rope with one end attached to a wall. When he starts moving the rope quickly, the frequency of the waves created on the rope doubles. What happens to the energy that is transferred to the wall when the frequency of the waves doubles?

Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.