a) One end of a string of length L is held fixed. The other end is attached to a weightless ring that can slide vertically up and down along a frictionless rod. b) Write down the wave function for this system for a standing wave of amplitude A and describe the boundary conditions. c) Apply the boundary conditions and derive two equations that identify both the allowed wavelengths and frequencies. You may assume that the wave speed for this system is v. d) Sketch the three standing waves that correspond to the three longest allowed wavelengths.