Cylindrical tube oriented vertically on Earth's surface, closed at the bottom and open at the top (height 100 m, cross sectional area 1 m2) initially contains air at a pressure of one atmosphere and temperature 300 K. A disc of mass m plugs the cylinder, but is free to slide up and down without friction. In equilibrium, the air in the cylinder is compressed to p = 2 atm while the air outside remains at 1 atm.
(a) What is the mass of the disc?
(b) Assuming that the temperature remains fixed and that dissipation can be ig- nored, what is the frequency with which the disc oscillates?