Auniform rope of length l and negligible stiffness hangs from a solid fixture in the ceiling. the free lower end of the rope is struck sharply at time t=0. what is the time t it takes the resulting wave on the rope to travel to the ceiling, be reflected, and return to the lower end of the rope?

Amichelson interferometer operating at a 600 nm wavelength has a 3.02-cm-long glass cell in one arm. to begin, the air is pumped out of the cell and mirror m2 is adjusted to produce a bright spot at the center of the interference pattern. then a valve is opened and air is slowly admitted into the cell. the index of refraction of air at 1.00 atm pressure is 1.00028.how many bright-dark-bright fringe shifts are observed as the cell fills with air?